# arXiv daily: Populations and Evolution (q-bio.PE)

##### 1.African swine fever in wild boar: investigating model assumptions and structure

**Authors:**Callum Shaw, Angus McLure, Kathryn Glass

**Abstract:** African swine fever (ASF) is a highly virulent viral disease that affects both domestic pigs and wild boar. Current ASF transmission in Europe is in part driven by wild boar populations, which act as a disease reservoir. Wild boar are abundant throughout Europe and are highly social animals with complex social organisation. Despite the known importance of wild boar in ASF spread and persistence, there remain knowledge gaps surrounding wild boar transmission. To investigate the influence of density-contact functions and wild boar social structure on disease dynamics, we developed a wild boar modelling framework. The framework included an ordinary differential equation model, a homogeneous stochastic model, and various network-based stochastic models that explicitly included wild boar social grouping. We found that power law functions (transmission $\propto$ density$^{0.5}$) and frequency-based density-contact functions were best able to reproduce recent Baltic outbreaks; however, power law function models predicted considerable carcass transmission, while frequency-based models had negligible carcass transmission. Furthermore, increased model heterogeneity caused a decrease in the relative importance of carcass-based transmission. The different dominant transmission pathways predicted by each model type affected the efficacy of potential interventions, which highlights the importance of evaluating model type and structure when modelling systems with uncertainties.

##### 1.Partial differential equation models for invasive species spread in the presence of spatial heterogeneity

**Authors:**Elliott Hughes, Miguel Moyers-Gonzalez, Rua Murray, Phillip L. Wilson

**Abstract:** Models of invasive species spread often assume that landscapes are spatially homogeneous; thus simplifying analysis but potentially reducing accuracy. We extend a recently developed partial differential equation model for invasive conifer spread to account for spatial heterogeneity in parameter values and introduce a method to obtain key outputs (e.g. spread rates) from computational simulations. Simulations produce patterns of spatial spread remarkably similar to observed patterns in grassland ecosystems invaded by exotic conifers, validating our spatially explicit strategy. We find that incorporating spatial variation in different parameters does not significantly affect the evolution of invasions (which are characterised by a long quiescent period followed by rapid evolution towards to a constant rate of invasion) but that distributional assumptions can have a significant impact on the spread rate of invasions. Our work demonstrates that spatial variation in site-suitability or other parameters can have a significant impact on invasions

##### 2.Do Species Evolve Through Mutations Guided by Non-Coding RNAs?

**Authors:**Reza Rahmanzadeh

**Abstract:** The current theory of evolution is almost the one Darwin and Wallace proposed two centuries ago and the following discoveries e.g., Mendelian genetics and neutral mutation theory have not made significant modifications. The current evolution theory relies mostly on heritable variations within species population, natural selection and genetic drift. The inability of the current theory to explain and predict biological observations, especially the emergence of evolutionary novelties, highlights the need to incorporate recent evolutionary, developmental and genetics findings in order to achieve a more comprehensive explanation of species evolution. The present paper provides significant body of evidence to substantiate a new theory to account for species evolution. The main axes of the proposed theory include: First, mutations leading to genetic novelties in a given species during evolution should be guided by the environment surrounding that species. Second, environment and germline are connected with each other via soma-germline messengers e.g., non-coding RNAs (ncRNAs). Third, based on the information that germline continuously receives in terms of epigenetic messengers three stages of heritable changes may occur in germline genome to produce more adaptable offspring: i, Epigenetic modifications, ii, Genetic mutations in the sequence of pre-existing genes in order to improve their potency, and iii, The production of new genes with distinct gene-coding regions, which may have their own regulatory regions.

##### 1.Social \textit{vs.} individual age-dependent costs of imperfect vaccination

**Authors:**Fabio A. C. C. Chalub, Paulo Doutor, Paula Patrício, Maria do Céu Soares

**Abstract:** In diseases with long-term immunity, vaccination is known to increase the average age at infection as a result of the decrease in the pathogen circulation. This implies that a vaccination campaign can have negative effects when a disease is more costly (financial or health-related costs) for higher ages. This work considers an age-structured population transmission model with imperfect vaccination. Our aim is to compare the social and individual costs of vaccination, assuming that disease costs are age-dependent. A model coupling pathogen deterministic dynamics for a population consisting of juveniles and adults, both assumed to be rational agents, is introduced. The parameter region for which vaccination has a positive social impact is fully characterized and the Nash equilibrium of the vaccination game is obtained. Finally, collective strategies designed to promote voluntary vaccination, without compromising social welfare, are discussed.

##### 2.Single-cell mutational burden distributions in birth-death processes

**Authors:**Christo Morison, Dudley Stark, Weini Huang

**Abstract:** Genetic mutations are footprints of cancer evolution and reveal critical dynamic parameters of tumour growth, which otherwise are hard to measure in vivo. The mutation accumulation in tumour cell populations has been described by various statistics, such as site frequency spectra (SFS) from bulk or single-cell data, as well as single-cell division distributions (DD) and mutational burden distributions (MBD). An integrated understanding of these distributions obtained from different sequencing information is important to illuminate the ecological and evolutionary dynamics of tumours, and requires novel mathematical and computational tools. We introduce dynamical matrices to analyse and unite the SFS, DD and MBD based on a birth-death process. Using the Markov nature of the model, we derive recurrence relations for the expectations of these three distributions. While recovering classic exact results in pure-birth cases for the SFS and the DD through our new framework, we also derive a new expression for the MBD as well as approximations for all three distributions when death is introduced, confirming our results with stochastic simulations. Moreover, we demonstrate a natural link between the SFS and the single-cell MBD, and show that the MBD can be regenerated through the DD. Surprisingly, the single-cell MBD is mainly driven by the stochasticity arising in the DD, rather than the extra stochasticity in the number of mutations at each cell division.

##### 1.The canonical equation of adaptive dynamics in individual-based models with power law mutation rates

**Authors:**Tobias Paul

**Abstract:** In this paper, we consider an individual-based model with power law mutation probability. In this setting, we use the large population limit with a subsequent ``small mutations'' limit to derive the canonical equation of adaptive dynamics. For a one-dimensional trait space this corresponds to well established results and we can formulate a criterion for evolutionary branching in the spirit of Champagnat and M\'el\'eard (2011). In higher dimensional trait spaces, we find that the speed at which the solution of the canonical equation moves through space is reduced due to mutations being restricted to the underlying grid on the trait space. However, as opposed to the canonical equation with rare mutations, we can explicitly calculate the path which the dominant trait will take without having to solve the equation itself.

##### 2.A novel algebraic approach to time-reversible evolutionary models

**Authors:**Marta Casanellas, Roser Homs Pons, Angélica Torres

**Abstract:** In the last years algebraic tools have been proven to be useful in phylogenetic reconstruction and model selection by means of the study of phylogenetic invariants. However, up to now, the models studied from an algebraic viewpoint are either too general or too restrictive (as group-based models with a uniform stationary distribution) to be used in practice. In this paper we provide a new framework to work with time-reversible models, which are the most widely used by biologists. In our approach we consider algebraic time-reversible models on phylogenetic trees (as defined by Allman and Rhodes) and introduce a new inner product to make all transition matrices of the process diagonalizable through the same orthogonal eigenbasis. This framework generalizes the Fourier transform widely used to work with group-based models and recovers some of the well known results. As illustration, we exploit the combination of our technique with algebraic geometry tools to provide relevant phylogenetic invariants for trees evolving under the Tamura-Nei model of nucleotide substitution.

##### 3.Projections of Economic Impacts of Climate Change on Marine Protected Areas: Palau, the Great Barrier Reef, and the Bering Sea

**Authors:**Talya ten Brink

**Abstract:** Climate change substantially impacts ecological systems. Marine species are shifting their distribution because of climate change towards colder waters, potentially compromising the benefits of currently established Marine Protected Areas (MPAs). Therefore, we demonstrate how three case study regions will be impacted by warming ocean waters to prepare stakeholders to understand how the fisheries around the MPAs is predicted to change. We chose the case studies to focus on large scale MPAs in i) a cold, polar region, ii) a tropical region near the equator, and iii) a tropical region farther from the equator. We quantify the biological impacts of shifts in species distribution due to climate change for fishing communities that depend on the Palau National Marine Sanctuary, the Great Barrier Reef Marine National Park Zone, and the North Bering Sea Research Area MPAs. We find that fisheries sectors will be impacted differently in different regions and show that all three regions can be supported by this methodology for decision making that joins sector income and species diversity.

##### 1.A scoping review of mathematical models of Plasmodium vivax

**Authors:**Md Nurul Anwar, Lauren Smith, Angela Devine, Somya Mehra, Camelia R. Walker, Elizabeth Ivory, Eamon Conway, Ivo Mueller, James M. McCaw, Jennifer A. Flegg, Roslyn I. Hickson

**Abstract:** Plasmodium vivax is one of the most geographically widespread malaria parasites in the world due to its ability to remain dormant in the human liver as hypnozoites and subsequently reactivate after the initial infection (i.e. relapse infections). More than 80% of P. vivax infections are due to hypnozoite reactivation. Mathematical modelling approaches have been widely applied to understand P. vivax dynamics and predict the impact of intervention outcomes. In this article, we provide a scoping review of mathematical models that capture P. vivax transmission dynamics published between January 1988 and May 2023 to provide a comprehensive summary of the mathematical models and techniques used to model P. vivax dynamics. We aim to assist researchers working on P. vivax transmission and other aspects of P. vivax malaria by highlighting best practices in currently published models and highlighting where future model development is required. We provide an overview of the different strategies used to incorporate the parasite's biology, use of multiple scales (within-host and population-level), superinfection, immunity, and treatment interventions. In most of the published literature, the rationale for different modelling approaches was driven by the research question at hand. Some models focus on the parasites' complicated biology, while others incorporate simplified assumptions to avoid model complexity. Overall, the existing literature on mathematical models for P. vivax encompasses various aspects of the parasite's dynamics. We recommend that future research should focus on refining how key aspects of P. vivax dynamics are modelled, including the accumulation of hypnozoite variation, the interaction between P. falciparum and P. vivax, acquisition of immunity, and recovery under superinfection.

##### 1.Substrate geometry affects population dynamics in a bacterial biofilm

**Authors:**Witold Postek, Klaudia Staskiewicz, Elin Lilja, Bartlomiej Waclaw

**Abstract:** Biofilms inhabit a range of environments, such as dental plaques or soil micropores, often characterized by intricate, non-even surfaces. However, the impact of surface irregularities on the population dynamics of biofilms remains elusive as most biofilm experiments are conducted on flat surfaces. Here, we show that the shape of the surface on which a biofilm grows influences genetic drift and selection within the biofilm. We culture E. coli biofilms in micro-wells with an undulating bottom surface and observe the emergence of clonal sectors whose size corresponds to that of the undulations, despite no physical barrier separating different areas of the biofilm. The sectors are remarkably stable over time and do not invade each other; we attribute this stability to the characteristics of the velocity field within the growing biofilm, which hinders mixing and clonal expansion. A microscopically-detailed computer model fully reproduces these findings and highlights the role of mechanical (physical) interactions such as adhesion and friction in microbial evolution. The model also predicts clonal expansion to be severely limited even for clones with a significant growth advantage - a finding which we subsequently confirm experimentally using a mixture of antibiotic-sensitive and antibiotic-resistant mutants in the presence of sub-lethal concentrations of the antibiotic rifampicin. The strong suppression of selection contrasts sharply with the behavior seen in bacterial colonies on agar commonly used to study range expansion and evolution in biofilms. Our results show that biofilm population dynamics can be controlled by patterning the surface, and demonstrate how a better understanding of the physics of bacterial growth can pave the way for new strategies in steering microbial evolution.

##### 1.How thermal priming of coral gametes shapes fertilization success

**Authors:**Antoine Puisay
CRIOBE, Laetitia Hédouin
CRIOBE, Rosanne Pilon
CRIOBE, Claire Goiran
CRIOBE, Benoit Pujol
CRIOBE

**Abstract:** Seawater temperature rise is damaging coral reef ecosystems. There is growing evidence for the negative impact of rising temperatures on the survival of adult corals and their reproductive success. However, the effect of elevated temperatures on gametes remains scarcely studied. Here we tested the effect of the thermal priming of gametes on the fertilization success in experimentally tested populations of Acropora cytherea corals in French Polynesia. As expected, a temperature of 30 {\textdegree}C (ambient +3 {\textdegree}C) reduces coral fertilization success. However, the thermal exposure of gametes to 30 {\textdegree}C after their release in seawater prior to fertilization limited fertilization failure, with a greater impact of oocytes in comparison to sperm. This temperature is similar to temperatures observed in nature under the changing climate. Our findings imply that the thermal priming of early life stages, such as gametes may play a role in maintaining the coral fertilization success in spite of increasing seawater temperature.

##### 2.Compartment model with retarded transition rates

**Authors:**Teo Granger, Thomas Michelitsch, Bernard Collet, Michael Bestehorn, Alejandro Riascos

**Abstract:** Our study is devoted to a four-compartment epidemic model of a constant population of independent random walkers. Each walker is in one of four compartments (S-susceptible, C-infected but not infectious (period of incubation), I-infected and infectious, R-recovered and immune) characterizing the states of health. The walkers navigate independently on a periodic 2D lattice. Infections occur by collisions of susceptible and infectious walkers. Once infected, a walker undergoes the delayed cyclic transition pathway S $\to$ C $\to$ I $\to$ R $\to$ S. The random delay times between the transitions (sojourn times in the compartments) are drawn from independent probability density functions (PDFs). We analyze the existence of the endemic equilibrium and stability of the globally healthy state and derive a condition for the spread of the epidemics which we connect with the basic reproduction number $R_0>1$. We give quantitative numerical evidence that a simple approach based on random walkers offers an appropriate microscopic picture of the dynamics for this class of epidemics.

##### 3.Coalescent processes emerging from large deviations in offspring numbers

**Authors:**Ethan Levien

**Abstract:** The classical model for the genealogies of a neutrally evolving population in a fixed is environment is due to Kingman. Kingman's coalescent process, which produces a binary tree, universally emerges from many microscopic models in which the variance in the number of offspring is finite. It is understood that power-law offspring distributions with infinite variance can result in a very different type of coalescent structure with merging of more than two lineages. Here we investigate the regime where the variance of the offspring distribution is finite but comparable to the population size. This is achieved by studying a model in which the logarithm offspring sizes has a stretched exponential form. Such offspring distributions are motivated by biology, where they emerges from a toy model of growth in a heterogenous environment, but also mathematics and statistical physics, where limit theorems and phase transitions for sums over random exponentials have seen considerable attention due to their appearance in the partition function of the Random Energy Model (REM). We find that the limit coalescent is a $\beta$-coalescent -- a previously studied model emerging from evolutionary dynamics models with heavy-tailed offspring distributions. We also discuss the interpretation of these results in terms of the REM.

##### 1.Outbreak-size distributions under fluctuating rates

**Authors:**Jason Hindes, Luis Mier-y-Teran-Romero, Ira B. Schwartz, Michael Assaf

**Abstract:** We study the effect of noisy infection (contact) and recovery rates on the distribution of outbreak sizes in the stochastic SIR model. The rates are modeled as Ornstein-Uhlenbeck processes with finite correlation time and variance, which we illustrate using outbreak data from the RSV 2019-2020 season in the US. In the limit of large populations, we find analytical solutions for the outbreak-size distribution in the long-correlated (adiabatic) and short-correlated (white) noise regimes, and demonstrate that the distribution can be highly skewed with significant probabilities for large fluctuations away from mean-field theory. Furthermore, we assess the relative contribution of demographic and reaction-rate noise on the outbreak-size variance, and show that demographic noise becomes irrelevant in the presence of slowly varying reaction-rate noise but persists for large system sizes if the noise is fast. Finally, we show that the crossover to the white-noise regime typically occurs for correlation times that are on the same order as the characteristic recovery time in the model.

##### 1.Predator-prey survival pressure is sufficient to evolve swarming behaviors

**Authors:**Jianan Li, Liang Li, Shiyu Zhao

**Abstract:** The comprehension of how local interactions arise in global collective behavior is of utmost importance in both biological and physical research. Traditional agent-based models often rely on static rules that fail to capture the dynamic strategies of the biological world. Reinforcement learning has been proposed as a solution, but most previous methods adopt handcrafted reward functions that implicitly or explicitly encourage the emergence of swarming behaviors. In this study, we propose a minimal predator-prey coevolution framework based on mixed cooperative-competitive multiagent reinforcement learning, and adopt a reward function that is solely based on the fundamental survival pressure, that is, prey receive a reward of $-1$ if caught by predators while predators receive a reward of $+1$. Surprisingly, our analysis of this approach reveals an unexpectedly rich diversity of emergent behaviors for both prey and predators, including flocking and swirling behaviors for prey, as well as dispersion tactics, confusion, and marginal predation phenomena for predators. Overall, our study provides novel insights into the collective behavior of organisms and highlights the potential applications in swarm robotics.

##### 1.A new multi-metric approach for quantifying global biodiscovery and conservation priorities reveals overlooked hotspots for amphibians

**Authors:**Sky Button, Amaël Borzée

**Abstract:** Undocumented species represent one of the largest hurdles for conservation efforts due to the uncertainty they introduce into conservation planning. Until the distribution of earth's biodiversity is better understood, substantial conjecture will continue to be required for protecting species from anthropogenic extinction. Therefore, we developed a novel approach for identifying regions with promising biodiscovery prospects, linked to integrative conservation priorities, which we illustrate using amphibians. Our approach builds on previous estimates of biodiscovery priorities by simultaneously (1) considering linkages between spatio-environmental variables and biodiversity, (2) accounting for the negative relationship between past sampling intensity and future biodiscovery potential, (3) incorporating a priori knowledge about global species distribution patterns, (4) addressing spatial autocorrelation in community composition, and (5) weighting theoretical undocumented species by their predicted levels of conservation need. Using boosted regression trees and 50km^2 map pixels spread across the global range of amphibians, we identified several regions likely to contain many undocumented amphibian species and conservation needs, including the Southeast Asian Archipelago, humid portions of sub-Saharan Africa, and undersampled portions of the Amazon, Andes Mountains, and Central America. We also ranked top-scoring ecoregions by their mean and maximum biodiscovery potential and found that the top-20 ranked ecoregions were most concentrated in the Southeast Asian Archipelago and tropical Africa for undocumented species richness, and in tropical Africa and tropical South America for integrative undocumented amphibian conservation needs. However, high-scoring pixels tended to be widely distributed across different ecoregions for both biodiscovery scoring approaches.

##### 2.A discrete-time dynamical model of prey and stage-structured predator with juvenile hunting incorporating negative effects of prey refuge

**Authors:**Debasish Bhattacharjee, Nabajit Ray, Dipam Das, Hemanta Kumar Sarmah

**Abstract:** This paper examines a discrete predator-prey model that incorporates prey refuge and its detrimental impact on the growth of the prey population. Age structure is taken into account for predator species. Furthermore, juvenile hunting as well as prey counter-attack are also considered. This paper provides a comprehensive analysis of the existence and stability conditions pertaining to all possible fixed points. The analytical and numerical investigation into the occurrence of different bifurcations, such as the Neimark-Sacker bifurcation and period-doubling bifurcation, in relation to various parameters is discussed. The impact of the parameters reflecting prey growth and prey refuge is thoroughly addressed. Numerous numerical simulations are presented in order to validate the theoretical findings.

##### 1.Evolving division of labor in a response threshold model

**Authors:**José F. Fontanari, Viviane M. de Oliveira, Paulo R. A. Campos

**Abstract:** The response threshold model explains the emergence of division of labor (i.e., task specialization) in an unstructured population by assuming that the individuals have different propensities to work on different tasks. The incentive to attend to a particular task increases when the task is left unattended and decreases when individuals work on it. Here we derive mean-field equations for the stimulus dynamics and show that they exhibit complex attractors through period-doubling bifurcation cascades when the noise disrupting the thresholds is small. In addition, we show how the fixed threshold can be set to ensure specialization in both the transient and equilibrium regimes of the stimulus dynamics. However, a complete explanation of the emergence of division of labor requires that we address the question of where the threshold variation comes from, starting from a homogeneous population. We then study a structured population scenario, where the population is divided into a large number of independent groups of equal size, and the fitness of a group is proportional to the weighted mean work performed on the tasks during a fixed period of time. Using a winner-take-all strategy to model group competition and assuming an initial homogeneous metapopulation, we find that a substantial fraction of workers specialize in each task, without the need to penalize task switching.

##### 1.Analysis of Insect-Plant Interactions Affected by Mining Operations, A Graph Mining Approach

**Authors:**Ali Bayat, Mohammad Heydari, Amir Albadvi

**Abstract:** The decline in ecological connections signifies the potential extinction of species, which can be attributed to disruptions and alterations. The decrease in interconnections among species reflects their susceptibility to changes. For example, certain insects and plants that rely on exclusive interactions with a limited number of species, or even a specific species, face the risk of extinction if they lose these crucial connections. Currently, mining activities pose significant harm to natural ecosystems, resulting in various adverse environmental impacts. In this study, we utilized network science techniques to analyze the ecosystem in a graph-based structure, aiming to conserve the ecosystem affected by mining operations in the northern region of Scotland. The research encompasses identifying the most vital members of the network, establishing criteria for identifying communities within the network, comparing, and evaluating them, using models to predict secondary extinctions that occur when a species is removed from the network, and assessing the extent of network damage. Our study's novelty is utilizing network science approaches to investigate the biological data related to interactions between insects and plants.

##### 1.The GeoLifeCLEF 2023 Dataset to evaluate plant species distribution models at high spatial resolution across Europe

**Authors:**Christophe Botella
ZENITH, Benjamin Deneu
ZENITH, Diego Marcos
ZENITH, Maximilien Servajean
ADVANSE, UPVM, Joaquim Estopinan
ZENITH, Théo Larcher
ZENITH, César Leblanc
ZENITH, Pierre Bonnet
UMR AMAP, Cirad-BIOS, Alexis Joly
ZENITH

**Abstract:** The difficulty to measure or predict species community composition at fine spatio-temporal resolution and over large spatial scales severely hampers our ability to understand species assemblages and take appropriate conservation measures. Despite the progress in species distribution modeling (SDM) over the past decades, SDM have just begun to integrate high resolution remote sensing data and their predictions are still entailed by many biases due to heterogeneity of the available biodiversity observations, most often opportunistic presence only data. We designed a European scale dataset covering around ten thousand plant species to calibrate and evaluate SDM predictions of species composition in space and time at high spatial resolution (~ten meters), and their spatial transferability. For model training, we extracted and harmonized five million heterogeneous presence-only records from selected GBIF datasets and 6 thousand exhaustive presence-absence surveys both sampled during 2017-2021. We associated species observations to diverse environmental rasters classically used in SDMs, as well as to 10 m resolution RGB and Near-Infra-Red satellite images and 20 years-time series of climatic variables and satellite point values. The evaluation dataset is based on 22 thousand standardized presence-absence surveys separated from the training set with a spatial block hold out procedure. The GeoLifeCLEF 2023 dataset is open access and the first benchmark for researchers aiming to improve the prediction of plant species composition at a very fine spatial grain and at continental scale. It is a space to explore new ways of combining massive and diverse species observations and environmental information at various scales. Innovative AI-based approaches, in particular, should be among the most interesting methods to experiment with on the GeoLifeCLEF 2023 dataset.

##### 2.The role of APOBEC3-induced mutations in the differential evolution of monkeypox virus

**Authors:**Xiangting Li, Sara Habibipour, Tom Chou, Otto O. Yang

**Abstract:** Recent studies show that newly sampled monkeypox virus (MPXV) genomes exhibit mutations consistent with Apolipoprotein B mRNA Editing Catalytic Polypeptide-like3 (APOBEC3)-mediated editing, compared to MPXV genomes collected earlier. It is unclear whether these single nucleotide polymorphisms (SNPs) result from APOBEC3-induced editing or are a consequence of genetic drift within one or more MPXV animal reservoirs. We develop a simple method based on a generalization of the General-Time-Reversible (GTR) model to show that the observed SNPs are likely the result of APOBEC3-induced editing. The statistical features allow us to extract lineage information and estimate evolutionary events.

##### 1.Local and extensive fluctuations in sparsely-interacting ecological communities

**Authors:**Stav Marcus, Ari M Turner, Guy Bunin

**Abstract:** Ecological communities with many species can be classified into dynamical phases. In systems with all-to-all interactions, a phase where a fixed point is always reached and a dynamically-fluctuating phase have been found. The dynamics when interactions are sparse, with each species interacting with only several others, has remained largely unexplored. Here we show that a new type of phase appears in the phase diagram, where for the same control parameters different communities may reach either a fixed point or a state where the abundances of a finite subset of species fluctuate, and calculate the probability for each outcome. These fluctuating species are organized around short cycles in the interaction graph, and their abundances undergo large non-linear fluctuations. We characterize the approach from this phase to a phase with extensively many fluctuating species, and show that the probability of fluctuations grows continuously to one as the transition is approached, and that the number of fluctuating species diverges. This is qualitatively distinct from the transition to extensive fluctuations coming from a fixed point phase, which is marked by a loss of linear stability. The differences are traced back to the emergent binary character of the dynamics when far away from short cycles in the local fluctuations phase.

##### 1.Modeling the effects of adherence to vaccination and health protocols in epidemic dynamics by means of an SIR model

**Authors:**Jasmin Nunuvero, Angelique Santiago, Moshe Cohen, Anca Radulescu

**Abstract:** Susceptible-Infected-Recovered (SIR) models have been used for decades to understand epidemic outbreak dynamics. We develop an SIR model specifically designed to study the effects of population behavior with respect to health and vaccination protocols in a generic epidemic. Through a collection of parameters, our model includes the traditional SIR components: population birth, death, infection, recovery and vaccination rates, as well as limited immunity. We first use this simple setup to compare the effects of two vaccination schemes, one in which people are vaccinated at a rate proportional with the population, and one in which vaccines are administered to a fraction of the susceptible people (both of which are know strategies in real life epidemics). We then expand on the model and the analysis by investigating how these two vaccination schemes hold under two scenarios of population behavior: one in which people abide by health protocols and work towards diminishing transmission when infection is high; one in which people relax health protocols when infection is high. We illustrate these two aspects (vaccination and adherence to health protocols) act together to control the epidemic outbreak. While it is ideal that the tow components act jointly, we also show that tight observance of health protocols may diminish the need for vaccination in the effort to clear or mitigate the outbreak. Conversely, an efficient vaccination strategy can compensate for some degree of laxity in people's behavior.

##### 1.Finite population effects on optimal communication for social foragers

**Authors:**Hyunjoong Kim, Yoichiro Mori, Joshua B Plotkin

**Abstract:** Foraging is crucial for animals to survive. Many species forage in groups, as individuals communicate to share information about the location of available resources. For example, eusocial foragers, such as honey bees and many ants, recruit members from their central hive or nest to a known foraging site. However, the optimal level of communication and recruitment depends on the overall group size, the distribution of available resources, and the extent of interference between multiple individuals attempting to forage from a site. In this paper, we develop a discrete-time Markov chain model of eusocial foragers, who communicate information with a certain probability. We compare the stochastic model and its corresponding infinite-population limit. We find that foraging efficiency tapers off when recruitment probability is too high -- a phenomenon that does not occur in the infinite-population model, even though it occurs for any finite population size. The marginal inefficiency at high recruitment probability increases as the population increases, similar to a boundary layer. In particular, we prove there is a significant gap between the foraging efficiency of finite and infinite population models in the extreme case of complete communication. We also analyze this phenomenon by approximating the stationary distribution of foragers over sites in terms of mean escape times from multiple quasi-steady states. We conclude that for any finite group of foragers, an individual who has found a resource should only sometimes recruit others to the same resource. We discuss the relationship between our analysis and multi-agent multi-arm bandit problems.

##### 1.Separable mixing: the general formulation and a particular example focusing on mask efficiency

**Authors:**M. C. J. Bootsma, K. M. D. Chan, O. Diekmann, H. Inaba

**Abstract:** The aim of this short note is twofold. We formulate the general Kermack-McKendrick epidemic model incorporating static heterogeneity and show how it simplifies to a scalar Renewal Equation (RE) when separable mixing is assumed. A key feature is that all information about the heterogeneity is encoded in one nonlinear real valued function of a real variable. Inspired by work of R. Pastor-Satorras and C. Castellano, we next investigate mask efficiency and demonstrate that it is straightforward to rederive from the RE their main conclusion, that the best way to protect the population as a whole is to protect yourself. Thus we establish that this conclusion is robust, in the sense that it also holds outside the world of network models.

##### 1.Quantifying the Influence of Climate on Human Mind and Culture: Evidence from Visual Art

**Authors:**Shuhei Kitamura

**Abstract:** This paper examines the influence of climate change on the human mind and culture from the 13th century to the 21st century. By quantitatively analyzing 100,000 paintings and the biological data of over 2,000 artists, an interesting U-shaped pattern in the lightness of paintings was found, which correlated with trends in global temperature. Event study analysis revealed that when an artist is subjected to a high-temperature shock, their paintings become brighter in later periods. Moreover, the effects are more pronounced in art genres that rely less on real things and more on the artist's imagination, indicating the influence of artists' minds. Overall, this study demonstrates the significant and enduring influence of climate on the human mind and culture over centuries.

##### 1.The persistence of bipartite ecological communities with Lotka-Volterra dynamics

**Authors:**Matthew Dopson, Clive Emary

**Abstract:** The assembly and persistence of ecological communities can be understood as the result of the interaction and migration of species. Here we study a single community subject to migration from a species pool in which inter-specific interactions are organised according to a bipartite network. Considering the dynamics of species abundances to be governed by generalised Lotka-Volterra equations, we extend work on unipartite networks to we derive exact results for the phase diagram of this model. Focusing on antagonistic interactions, we describe factors that influence the persistence of the two guilds, locate transitions to multiple-attractor and unbounded phases, as well identify a region of parameter space in which consumers are essentially absent in the local community.

##### 1.Unlocking ensemble ecosystem modelling for large and complex networks

**Authors:**Sarah A. Vollert, Christopher Drovandi, Matthew P. Adams

**Abstract:** The potential effects of conservation actions on threatened species can be predicted using ensemble ecosystem models. These model ensembles commonly assume stable coexistence of species in the absence of available data. However, existing ensemble-generation methods become computationally inefficient as the size of the ecosystem network increases, preventing larger networks from being studied. We present a novel sequential Monte Carlo sampling approach for ensemble generation that is orders of magnitude faster than existing approaches. We demonstrate that the methods produce equivalent parameter inferences, model predictions, and tightly constrained parameter combinations using a novel sensitivity analysis method. For one case study, we demonstrate a speed-up from 108 days to 6 hours, while maintaining equivalent ensembles. Now, for the first time, larger and more realistic networks can be practically simulated.

##### 1.Selected Topics of Social Physics: Nonequilibrium Systems

**Authors:**V. I. Yukalov

**Abstract:** This review article is the second part of the project ``Selected Topics of Social Physics". The first part has been devoted to equilibrium systems. The present part considers nonequilibrium systems. The style of the paper combines the features of a tutorial and a review, which, from one side, makes it easy to read for nonspecialists aiming at grasping the basics of social physics, and from the other side, describes several rather recent original models containing new ideas that could be of interest to experienced researchers in the field. The present material is based on the lectures that the author had been giving during several years at the Swiss Federal Institute of Technology in Zurich (ETH Zurich).

##### 2.Soft trade-offs and the stochastic emergence of diversification in E. coli evolution experiments

**Authors:**Roberto Corral López, Samir Suweis, Sandro Azaele, Miguel A. Muñoz

**Abstract:** Laboratory experiments of bacterial colonies (e.g., \emph{Escherichia coli}) under well-controlled conditions often lead to evolutionary diversification in which (at least) two ecotypes, each one specialized in the consumption of a different set of metabolic resources, branch out from an initially monomorphic population. Empirical evidence suggests that, even under fixed and stable conditions, such an ``evolutionary branching'' occurs in a stochastic way, meaning that: (i) it is observed in a significant fraction, but not all, of the experimental repetitions, (ii) it may emerge at broadly diverse times, and (iii) the relative abundances of the resulting subpopulations are variable across experiments. Theoretical approaches shedding light on the possible emergence of evolutionary branching in this type of conditions have been previously developed within the theory of ``adaptive dynamics''. Such approaches are typically deterministic -- or incorporate at most demographic or finite-size fluctuations which become negligible for the extremely large populations of these experiments -- and, thus, do not permit to reproduce the empirically observed large degree of variability. Here, we make further progress and shed new light on the stochastic nature of evolutionary outcomes by introducing the idea of ``soft'' trade-offs (as opposed to ``hard'' ones). This introduces a natural new source of stochasticity which allows one to account for the empirically observed variability as well as to make predictions for the likelihood of evolutionary branching to be observed, thus helping to bridge the gap between theory and experiments.

##### 1.Extinction time distributions of populations and genotypes

**Authors:**David Kessler, Nadav M. Shnerb

**Abstract:** In the long run, the eventual extinction of any biological population is an inevitable outcome. While extensive research has focused on the average time it takes for a population to go extinct under various circumstances, there has been limited exploration of the distributions of extinction times and the likelihood of significant fluctuations. Recently, Hathcock and Strogatz [PRL 128, 218301 (2022)] identified Gumbel statistics as a universal asymptotic distribution for extinction-prone dynamics in a stable environment. In this study, we aim to provide a comprehensive survey of this problem by examining a range of plausible scenarios, including extinction-prone, marginal (neutral), and stable dynamics. We consider the influence of demographic stochasticity, which arises from the inherent randomness of the birth-death process, as well as cases where stochasticity originates from the more pronounced effect of random environmental variations. Our work proposes several generic criteria that can be used for the classification of experimental and empirical systems, thereby enhancing our ability to discern the mechanisms governing extinction dynamics. By employing these criteria, we can improve our understanding of the underlying mechanisms driving extinction processes.

##### 2.The weighted total cophenetic index: A novel balance index for phylogenetic networks

**Authors:**Linda Knüver, Mareike Fischer, Marc Hellmuth, Kristina Wicke

**Abstract:** Phylogenetic networks play an important role in evolutionary biology as, other than phylogenetic trees, they can be used to accommodate reticulate evolutionary events such as horizontal gene transfer and hybridization. Recent research has provided a lot of progress concerning the reconstruction of such networks from data as well as insight into their graph theoretical properties. However, methods and tools to quantify structural properties of networks or differences between them are still very limited. For example, for phylogenetic trees, it is common to use balance indices to draw conclusions concerning the underlying evolutionary model, and more than twenty such indices have been proposed and are used for different purposes. One of the most frequently used balance index for trees is the so-called total cophenetic index, which has several mathematically and biologically desirable properties. For networks, on the other hand, balance indices are to-date still scarce. In this contribution, we introduce the \textit{weighted} total cophenetic index as a generalization of the total cophenetic index for trees to make it applicable to general phylogenetic networks. As we shall see, this index can be determined efficiently and behaves in a mathematical sound way, i.e., it satisfies so-called locality and recursiveness conditions. In addition, we analyze its extremal properties and, in particular, we investigate its maxima and minima as well as the structure of networks that achieve these values within the space of so-called level-$1$ networks. We finally briefly compare this novel index to the two other network balance indices available so-far.

##### 1.Mean-field interacting multi-type birth-death processes with a view to applications in phylodynamics

**Authors:**William S. DeWitt, Steven N. Evans, Ella Hiesmayr, Sebastian Hummel

**Abstract:** Multi-type birth-death processes underlie approaches for inferring evolutionary dynamics from phylogenetic trees across biological scales, ranging from deep-time species macroevolution to rapid viral evolution and somatic cellular proliferation. A limitation of current phylogenetic birth-death models is that they require restrictive linearity assumptions that yield tractable likelihoods, but that also preclude interactions between individuals. Many fundamental evolutionary processes -- such as environmental carrying capacity or frequency-dependent selection -- entail interactions, and may strongly influence the dynamics in some systems. Here, we introduce a multi-type birth-death process in mean-field interaction with an ensemble of replicas of the focal process. We prove that, under quite general conditions, the ensemble's stochastically evolving interaction field converges to a deterministic trajectory in the limit of an infinite ensemble. In this limit, the replicas effectively decouple, and self-consistent interactions appear as nonlinearities in the infinitesimal generator of the focal process. We investigate a special case that is amenable to calculations in the context of a phylogenetic birth-death model, and is rich enough to model both carrying capacity and frequency-dependent selection.

##### 2.Forward hysteresis and Hopf bifurcation in an NPZD model with application to harmful algal blooms

**Authors:**Joshua C. Macdonald, Hayriye Gulbudak

**Abstract:** Nutrient-Phytoplankton-Zooplankton-Detritus (NPZD) models, describing the interactions between phytoplankton, zooplankton systems, and their ecosystem, are used to predict their ecological and evolutionary population dynamics. These organisms form the base two trophic levels of aquatic ecosystems. Hence understanding their population dynamics and how disturbances can affect these systems is crucial. Here, starting from a base NPZ modeling framework, we incorporate the harmful effects of phytoplankton overpopulation on zooplankton - representing a crucial next step in harmful algal bloom (HAB) modeling - and split the nutrient compartment to formulate an NPZD model. We then mathematically analyze the NPZ system upon which this new model is based, including local and global stability of equilibria, Hopf bifurcation condition, and forward hysteresis, where the bi-stability occurs with multiple attractors. Finally, we extend the threshold analysis to the NPZD model, which displays both forward hysteresis with bi-stability and Hopf bifurcation under different parameter regimes, and examine ecological implications after incorporating seasonality and ecological disturbances. Ultimately, we quantify ecosystem health in terms of the relative values of the robust persistence thresholds for phytoplankton and zooplankton and find (i) ecosystems sufficiently favoring phytoplankton, as quantified by the relative values of the plankton persistence numbers, are vulnerable to both HABs and (local) zooplankton extinction (ii) even healthy ecosystems are extremely sensitive to nutrient depletion over relatively short time scales.

##### 3.Coexistence of Competing Microbial Strains under Twofold Environmental Variability and Demographic Fluctuations

**Authors:**Matthew Asker, Lluís Hernández-Navarro, Alastair M. Rucklidge, Mauro Mobilia

**Abstract:** Microbial populations generally evolve in volatile environments, under conditions fluctuating between harsh and mild, e.g. as the result of sudden changes in toxin concentration or nutrient abundance. Environmental variability thus shapes the population long-time dynamics, notably by influencing the ability of different strains of microorganisms to coexist. Inspired by the evolution of antimicrobial resistance, we study the dynamics of a community consisting of two competing strains subject to twofold environmental variability. The level of toxin varies in time, favouring the growth of one strain under low levels and the other strain when the toxin level is high. We also model time-changing resource abundance by a randomly switching carrying capacity that drives the fluctuating size of the community. While one strain dominates in a static environment, we show that species coexistence is possible in the presence of environmental variability. By computational and analytical means, we determine the environmental conditions under which long-lived coexistence is possible and when it is almost certain. We also determine how the make-up of the coexistence phase and the average abundance of each strain depend on the environmental variability.

##### 4.Coupled environmental and demographic fluctuations shape the evolution of cooperative antimicrobial resistance

**Authors:**Lluís Hernández-Navarro, Matthew Asker, Alastair M. Rucklidge, Mauro Mobilia

**Abstract:** There is a pressing need to better understand how microbial populations respond to antimicrobial drugs, and to find mechanisms to possibly eradicate antimicrobial-resistant cells. The inactivation of antimicrobials by resistant microbes can often be viewed as a cooperative behavior leading to the coexistence of resistant and sensitive cells in large populations and static environments. This picture is however greatly altered by the fluctuations arising in volatile environments, in which microbial communities commonly evolve. Here, we study the eco-evolutionary dynamics of a population consisting of an antimicrobial resistant strain and microbes sensitive to antimicrobial drugs in a time-fluctuating environment, modeled by a carrying capacity randomly switching between states of abundance and scarcity. We assume that antimicrobial resistance is a shared public good when the number of resistant cells exceeds a certain threshold. Eco-evolutionary dynamics is thus characterized by demographic noise (birth and death events) coupled to environmental fluctuations which can cause population bottlenecks. By combining analytical and computational means, we determine the environmental conditions for the long-lived coexistence and fixation of both strains, and characterize a fluctuation-driven antimicrobial resistance eradication mechanism, where resistant microbes experience bottlenecks leading to extinction. We also discuss the possible applications of our findings to laboratory-controlled experiments.

##### 1.Analysis of a competitive respiratory disease system with quarantine

**Authors:**Anna Daniel Fome, Wolfgang Bock, Axel Klar

**Abstract:** In the world of epidemics, the mathematical modeling of disease co-infection is gaining importance due to its contributions to mathematics and public health. Because the co-infection may have a double burden on families, countries, and the universe, understanding its dynamics is paramount. We study a SEIQR (susceptible-exposed-infectious-quarantined-recovered) deterministic epidemic model with a single host population and multiple strains (-$c$ and -$i$) to account for two competitive diseases with quarantine effects. To model the role of quarantine and isolation efficacy in disease dynamics, we utilize a linear function. Further, we shed light on the standard endemic threshold and determine the conditions for extinction or coexistence with and without forming co-infection. Next, we show the dependence of the criticality based on specific parameters of the different pathogens. We found that the disease-free equilibrium (DFE) of the single-strain model always exists and is globally asymptotically stable (GAS) if $\tilde{\mathcal{R}}_k^q\leq 1$, else, a stable endemic equilibrium. On top of that, the model has forward bifurcation at $\tilde{\mathcal{R}}_k^q = 1$. In the case of a two-strain model, the strain with a large reproduction number outcompetes the one with a smaller reproduction number. Further, if the co-infected quarantine reproduction number is less than one, the infections of already infected individuals will die out, and co-infection will persist in the population otherwise. We note that the quarantine and isolation of exposed and infected individuals will reduce the number of secondary cases below one, consequently reducing the disease complications if the total number of people in the quarantine is at most the critical value.

##### 1.Differences between the true reproduction number and the apparent reproduction number of an epidemic time series

**Authors:**Oliver Eales, Steven Riley

**Abstract:** The time-varying reproduction number $R(t)$ measures the number of new infections per infectious individual and is closely correlated with the time series of infection incidence by definition. The timings of actual infections are rarely known, and analysis of epidemics usually relies on time series data for other outcomes such as symptom onset. A common implicit assumption, when estimating $R(t)$ from an epidemic time series, is that $R(t)$ has the same relationship with these downstream outcomes as it does with the time series of incidence. However, this assumption is unlikely to be valid given that most epidemic time series are not perfect proxies of incidence. Rather they represent convolutions of incidence with uncertain delay distributions. Here we define the apparent time-varying reproduction number, $R_A(t)$, the reproduction number calculated from a downstream epidemic time series and demonstrate how differences between $R_A(t)$ and $R(t)$ depend on the convolution function. The mean of the convolution function sets a time offset between the two signals, whilst the variance of the convolution function introduces a relative distortion between them. We present the convolution functions of epidemic time series that were available during the SARS-CoV-2 pandemic. Infection prevalence, measured by random sampling studies, presents fewer biases than other epidemic time series. Here we show that additionally the mean and variance of its convolution function were similar to that obtained from traditional surveillance based on mass-testing and could be reduced using more frequent testing, or by using stricter thresholds for positivity. Infection prevalence studies continue to be a versatile tool for tracking the temporal trends of $R(t)$, and with additional refinements to their study protocol, will be of even greater utility during any future epidemics or pandemics.

##### 2.Persistent disruption of interspecific competition after ultra-low esfenvalerate exposure

**Authors:**Florian Schunck, Matthias Liess

**Abstract:** Field and mesocosm studies repeatedly show that higher tier process reduce the predictive accuracy of toxicity evaluation and consequently their value for pesticide risk assessment. Therefore, understanding the influence of ecological complexity on toxicant effects is crucial to improve realism of aquatic risk assessment. Here we investigate the influence of repeated exposure to ecologically realistic concentrations of esfenvalerate on the similarly sensitive species Daphnia magna and Culex pipiens in a food limited and highly competitive environment. We show that significant perturbations in population development are only present close to the EC50. In contrast, interspecific competition between species is already reduced at concentrations 3-4 orders of magnitude below the acute EC50. We conclude that extremely low, environmentally relevant concentrations can disrupt species interactions. This toxicant mediated alteration of competitive balances in ecological communities may be the underlying mechanism for shifts in species distribution at ultra-low pesticide concentrations. A realistic risk assessment should therefore consider these processes in order to predict potential pesticide effects on the structure of communities.

##### 1.Generalized Lotka-Volterra Systems with Time Correlated Stochastic Interactions

**Authors:**Samir Suweis, Francesco Ferraro, Sandro Azaele, Amos Maritan

**Abstract:** The dynamics of species communities are typically modelled considering fixed parameters for species interactions. The problem of over-parameterization that ensues when considering large communities has been overcome by sampling species interactions from a probability distribution. However, species interactions are not fixed in time, but they can change on a time scale comparable to population dynamics. Here we investigate the impact of time-dependent species interactions using the generalized Lotka-Volterra model, which serves as a paradigmatic theoretical framework in several scientific fields. In this work we model species interactions as stochastic colored noise. Assuming a large number of species and a steady state, we obtain analytical predictions for the species abundance distribution, which matches well empirical observations. In particular, our results suggest the absence of extinctions, unlike scenarios with fixed species interactions.

##### 1.Genomic Informational Field Theory (GIFT) to characterize genotypes involved in large phenotypic fluctuations

**Authors:**Cyril Rauch, Panagiota Kyratzi, Andras Paldi

**Abstract:** Based on the normal distribution and its properties, i.e., average and variance, Fisher works have provided a conceptual framework to identify genotype-phenotype associations. While Fisher intuition has proved fruitful over the past century, the current demands for higher mapping precisions have led to the formulation of a new genotype-phenotype association method a.k.a. GIFT (Genomic Informational Field Theory). Not only is the method more powerful in extracting information from genotype and phenotype datasets, GIFT can also deal with any phenotype distribution density function. Here we apply GIFT to a hypothetical Cauchy-distributed phenotype. As opposed to the normal distribution that restricts fluctuations to a finite variance defined by the bulk of the distribution, Cauchy distribution embraces large phenotypic fluctuations and as a result, averages and variances from Cauchy-distributed phenotypes cannot be defined mathematically. While classic genotype-phenotype association methods (GWAS) are unable to function without proper average and variance, it is demonstrated here that GIFT can associate genotype to phenotype in this case. As phenotypic plasticity, i.e., phenotypic fluctuation, is central to surviving sudden environmental changes, by applying GIFT the unique characteristic of the genotype permitting evolution of biallelic organisms to take place is determined in this case.

##### 2.On the connections between the spatial Lambda-Fleming-Viot model and other processes for analysing geo-referenced genetic data

**Authors:**Johannes Wirtz, Stéphane Guindon

**Abstract:** The introduction of the spatial Lambda-Fleming-Viot model (LV) in population genetics was mainly driven by the pioneering work of Alison Etheridge, in collaboration with Nick Barton and Amandine V\'eber about ten years ago (1,2). The LV model provides a sound mathematical framework for describing the evolution of a population of related individuals along a spatial continuum. It alleviates the "pain in the torus" issue with Wright and Mal\'ecot's isolation by distance model and is sampling consistent, making it a tool of choice for statistical inference. Yet, little is known about the potential connections between the LV and other stochastic processes generating trees and the spatial coordinates along the corresponding lineages. This work focuses on a version of the LV whereby lineages move infinitely rapidly over infinitely small distances. Using simulations, we show that the induced LV tree-generating process is well approximated by a birth-death model. Our results also indicate that Brownian motions modelling the movements of lineages along birth-death trees do not generally provide a good approximation of the LV due to habitat boundaries effects that play an increasingly important role in the long run. Finally, we describe efficient algorithms for fast simulation of the backward and forward in time versions of the LV model.

##### 3.Unification of species, gene, and cell trees for single-cell expression analyses

**Authors:**Samuel H. Church, Jasmine L. Mah, Casey W. Dunn

**Abstract:** Comparisons of single-cell RNA sequencing (scRNA-seq) data across species can reveal links between cellular gene expression and the evolution of cell functions, features, and phenotypes. These comparisons invoke evolutionary histories, as depicted with phylogenetic trees, that define relationships between species, genes, and cells. Here we illustrate a tree-based framework for comparing scRNA-seq data, and contrast this framework with existing methods. We describe how we can use trees to identify homologous and comparable groups of genes and cells, based on their predicted relationship to genes and cells present in the common ancestor. We advocate for mapping data to branches of phylogenetic trees to test hypotheses about the evolution of cellular gene expression. We describe the kinds of data that can be compared, and the types of questions that each comparison has the potential to address. Finally, we reconcile species phylogenies, gene phylogenies, cell phylogenies, and cell lineages as different representations of the same concept: the tree of cellular life. By integrating phylogenetic approaches into scRNA-seq analyses, we can overcome challenges for building informed comparisons across species, and robustly test hypotheses about gene and cell evolution.

##### 1.Coping with seasons: evolutionary dynamics of gene networks in a changing environment

**Authors:**Csenge Petak, Lapo Frati, Melissa H. Pespeni, Nick Cheney

**Abstract:** In environments that vary frequently and unpredictably, bet-hedgers can overtake the population. Diversifying bet-hedgers have a diverse set of offspring so that, no matter the conditions they find themselves in, at least some offspring will have high fitness. In contrast, conservative bet-hedgers have a set of offspring that all have an in-between phenotype compared to the specialists. Here, we use an evolutionary algorithm of gene regulatory networks to de novo evolve the two strategies and investigate their relative success in different parameter settings. We found that diversifying bet-hedgers almost always evolved first, but then eventually got outcompeted by conservative bet-hedgers. We argue that even though similar selection pressures apply to the two bet-hedger strategies, conservative bet-hedgers could win due to the robustness of their evolved networks, in contrast to the sensitive networks of the diversifying bet-hedgers. These results reveal an unexplored aspect of the evolution of bet-hedging that could shed more light on the principles of biological adaptation in variable environmental conditions.

##### 1.Imputing phylogenetic trees using tropical polytopes over the space of phylogenetic trees

**Authors:**Ruriko Yoshida

**Abstract:** When we apply comparative phylogenetic analyses to genome data, it is a well-known problem and challenge that some of given species (or taxa) often have missing genes. In such a case, we have to impute a missing part of a gene tree from a sample of gene trees. In this short paper we propose a novel method to infer a missing part of a phylogenetic tree using an analogue of a classical linear regression in the setting of tropical geometry. In our approach, we consider a tropical polytope, a convex hull with respect to the tropical metric closest to the data points. We show a condition that we can guarantee that an estimated tree from our method has at most four Robinson-Foulds (RF) distance from the ground truth and computational experiments with simulated data show our method works well.

##### 1.Survival, extinction, and interface stability in a two--phase moving boundary model of biological invasion

**Authors:**Matthew J Simpson, Nizhum Rahman, Scott W McCue, Alexander KY Tam

**Abstract:** We consider a moving boundary mathematical model of biological invasion. The model describes the spatiotemporal evolution of two populations: each population undergoes linear diffusion and logistic growth, and the boundary between the two populations evolves according to a two--phase Stefan condition. This mathematical model describes situations where one population invades into regions occupied by the other population, such as the spreading of a malignant tumour into surrounding tissues. Full time--dependent numerical solutions are obtained using a level--set numerical method. We use these numerical solutions to explore several properties of the model including: (i) survival and extinction of one population initially surrounded by the other; and (ii) linear stability of the moving front boundary in the context of a travelling wave solution subjected to transverse perturbations. Overall, we show that many features of the well--studied one--phase single population analogue of this model can be very different in the more realistic two--phase setting. These results are important because realistic examples of biological invasion involve interactions between multiple populations and so great care should be taken when extrapolating predictions from a one--phase single population model to cases for which multiple populations are present. Open source Julia--based software is available on GitHub to replicate all results in this study.

##### 2.Evaluating The Impact Of Species Specialisation On Ecological Network Robustness Using Analytic Methods

**Authors:**Chris Jones, Damaris Zurell, Karoline Wiesner

**Abstract:** Ecological networks describe the interactions between different species, informing us of how they rely on one another for food, pollination and survival. If a species in an ecosystem is under threat of extinction, it can affect other species in the system and possibly result in their secondary extinction as well. Understanding how (primary) extinctions cause secondary extinctions on ecological networks has been considered previously using computational methods. However, these methods do not provide an explanation for the properties which make ecological networks robust, and can be computationally expensive. We develop a new analytic model for predicting secondary extinctions which requires no non-deterministic computational simulation. Our model can predict secondary extinctions when primary extinctions occur at random or due to some targeting based on the number of links per species or risk of extinction, and can be applied to an ecological network of any number of layers. Using our model, we consider how false positives and negatives in network data affect predictions for network robustness. We have also extended the model to predict scenarios in which secondary extinctions occur once species lose a certain percentage of interaction strength, and to model the loss of interactions as opposed to just species extinction. From our model, it is possible to derive new analytic results such as how ecological networks are most robust when secondary species degree variance is minimised. Additionally, we show that both specialisation and generalisation in distribution of interaction strength can be advantageous for network robustness, depending upon the extinction scenario being considered.

##### 1.Measuring unequal distribution of pandemic severity across census years, variants of concern and interventions

**Authors:**Quang Dang Nguyen, Sheryl L. Chang, Christina M. Jamerlan, Mikhail Prokopenko

**Abstract:** Diverse and complex intervention policies deployed over the last years have shown varied effectiveness in controlling the COVID-19 pandemic. However, a systematic analysis and modelling of the combined effects of different viral lineages and complex intervention policies remains a challenge. Using large-scale agent-based modelling and a high-resolution computational simulation matching census-based demographics of Australia, we carried out a systematic comparative analysis of several COVID-19 pandemic scenarios. The scenarios covered two most recent Australian census years (2016 and 2021), three variants of concern (ancestral, Delta and Omicron), and five representative intervention policies. In addition, we introduced pandemic Lorenz curves measuring an unequal distribution of the pandemic severity across local areas. We quantified nonlinear effects of population heterogeneity on the pandemic severity, highlighting that (i) the population growth amplifies pandemic peaks, (ii) the changes in population size amplify the peak incidence more than the changes in density, and (iii) the pandemic severity is distributed unequally across local areas. We also examined and delineated the effects of urbanisation on the incidence bimodality, distinguishing between urban and regional pandemic waves. Finally, we quantified and examined the impact of school closures, complemented by partial interventions, and identified the conditions when inclusion of school closures may decisively control the transmission. Our results suggest that (a) public health response to long-lasting pandemics must be frequently reviewed and adapted to demographic changes, (b) in order to control recurrent waves, mass-vaccination rollouts need to be complemented by partial NPIs, and (c) healthcare and vaccination resources need to be prioritised towards the localities and regions with high population growth and/or high density.

##### 1.Impacts of seasonality and parasitism on honey bee population dynamics

**Authors:**Jun Chen, Jordy O Rodriguez Rincon, Gloria DeGrandi-Hoffman, Jennifer Fewell, Jon Harrison, Yun Kang

**Abstract:** The honeybee plays an extremely important role in ecosystem stability and diversity and in the production of bee pollinated crops. Honey bees and other pollinators are under threat from the combined effects of nutritional stress, parasitism, pesticides, and climate change that impact the timing, duration, and variability of seasonal events. To understand how parasitism and seasonality influence honey bee colonies separately and interactively, we developed a non-autonomous nonlinear honeybee-parasite interaction differential equation model that incorporates seasonality into the egg-laying rate of the queen. Our theoretical results show that parasitism negatively impacts the honey bee population either by decreasing colony size or destabilizing population dynamics through supercritical or subcritical Hopf-bifurcations depending on conditions. Our bifurcation analysis and simulations suggest that seasonality alone may have positive or negative impacts on the survival of honey bee colonies. More specifically, our study indicates that (1) the timing of the maximum egg-laying rate seems to determine when seasonality has positive or negative impacts; and (2) when the period of seasonality is large it can lead to the colony collapsing. Our study further suggests that the synergistic influences of parasitism and seasonality can lead to complicated dynamics that may positively and negatively impact the honey bee colony's survival. Our work partially uncovers the intrinsic effects of climate change and parasites, which potentially provide essential insights into how best to maintain or improve a honey bee colony's health.

##### 2.Unveiling the dynamics of canard cycles and global behaviour in a singularly perturbed predator-prey system with Allee effect in predator

**Authors:**Tapan Saha, Pallav Jyoti Pal

**Abstract:** In this article, we have considered a planar slow-fast modified Leslie-Gower predator-prey model with a weak Allee effect in the predator, based on the natural assumption that the prey reproduces far more quickly than the predator. We present a thorough mathematical analysis demonstrating the existence of homoclinic orbits, heteroclinic orbits, singular Hopf bifurcation, canard limit cycles, relaxation oscillations, the birth of canard explosion by combining the normal form theory of slow-fast systems, Fenichel's theorem and blow-up technique near non-hyperbolic point. We have obtained very rich dynamical phenomena of the model, including the saddle-node, Hopf, transcritical bifurcation, generalized Hopf, cusp point, homoclinic orbit, heteroclinic orbit, and Bogdanov-Takens bifurcations. Moreover, we have investigated the global stability of the unique positive equilibrium, as well as bistability, which shows that the system can display either 'prey extinction', 'stable coexistence', or 'oscillating coexistence' depending on the initial population size and values of the system parameters. The theoretical findings are verified by numerical simulations.

##### 3.Artificial Neural Network Prediction of COVID-19 Daily Infection Count

**Authors:**Ning Jiang, Charles Kolozsvary, Yao Li

**Abstract:** It is well known that the confirmed COVID-19 infection is only a fraction of the true fraction. In this paper we use an artificial neural network to learn the connection between the confirmed infection count, the testing data, and the true infection count. The true infection count in the training set is obtained by backcasting from the death count and the infection fatality ratio (IFR). Multiple factors are taken into consideration in the estimation of IFR. We also calibrate the recovered true COVID-19 case count with an SEIR model.

##### 4.Large system population dynamics with non-Gaussian interactions

**Authors:**Sandro Azaele, Amos Maritan

**Abstract:** We investigate the Generalized Lotka-Volterra (GLV) equations, a central model in theoretical ecology, where species interactions are assumed to be fixed over time and heterogeneous (quenched noise). Recent studies have suggested that the stability properties and abundance distributions of large disordered GLV systems depend, in the simplest scenario, solely on the mean and variance of the distribution of species interactions. However, empirical communities deviate from this level of universality. In this article, we present a generalized version of the dynamical mean field theory for non-Gaussian interactions that can be applied to various models, including the GLV equations. Our results show that the generalized mean field equations have solutions which depend on all cumulants of the distribution of species interactions, leading to a breakdown of universality. We leverage on this informative breakdown to extract microscopic interaction details from the macroscopic distribution of densities which are in agreement with empirical data. Specifically, in the case of sparse interactions, which we analytically investigate, we establish a simple relationship between the distribution of interactions and the distribution of species population densities.

##### 5.Optimal Vaccination Policy to Prevent Endemicity: A Stochastic Model

**Authors:**Félix Foutel-Rodier, Arthur Charpentier, Hélène Guérin

**Abstract:** We examine here the effects of recurrent vaccination and waning immunity on the establishment of an endemic equilibrium in a population. An individual-based model that incorporates memory effects for transmission rate during infection and subsequent immunity is introduced, considering stochasticity at the individual level. By letting the population size going to infinity, we derive a set of equations describing the large scale behavior of the epidemic. The analysis of the model's equilibria reveals a criterion for the existence of an endemic equilibrium, which depends on the rate of immunity loss and the distribution of time between booster doses. The outcome of a vaccination policy in this context is influenced by the efficiency of the vaccine in blocking transmissions and the distribution pattern of booster doses within the population. Strategies with evenly spaced booster shots at the individual level prove to be more effective in preventing disease spread compared to irregularly spaced boosters, as longer intervals without vaccination increase susceptibility and facilitate more efficient disease transmission. We provide an expression for the critical fraction of the population required to adhere to the vaccination policy in order to eradicate the disease, that resembles a well-known threshold for preventing an outbreak with an imperfect vaccine. We also investigate the consequences of unequal vaccine access in a population and prove that, under reasonable assumptions, fair vaccine allocation is the optimal strategy to prevent endemicity.

##### 6.Many-species ecological fluctuations as a jump process from the brink of extinction

**Authors:**Thibaut Arnoulx de Pirey, Guy Bunin

**Abstract:** Many-species ecological communities can exhibit persistent fluctuations driven by species interactions. These dynamics feature many interesting properties, such as the emergence of long timescales and large fluctuations, that have remained poorly understood. We look at such dynamics, when species are supported by migration at a small rate. We find that the dynamics are characterized by a single long correlation timescale. We prove that the time and abundances can be rescaled to yield a well-defined limiting process when the migration rate is small but positive. The existence of this rescaled dynamics predicts scaling forms for both abundance distributions and timescales, which are verified exactly in scaling collapse of simulation results. In the rescaled process, a clear separation naturally emerges at any given time between rare and abundant species, allowing for a clear-cut definition of the number of coexisting species. Species move back and forth between the rare and abundant subsets. The dynamics of a species entering the abundant subset starts with rapid growth from rare, appearing as an instantaneous jump in rescaled time, followed by meandering abundances with an overall negative bias. The emergence of the long timescale is explained by another rescaling theory for earlier times. Finally, we prove that the number of abundant species is tuned to remain below and without saturating a well-known stability bound, maintaining the system away from marginality. This is traced back to the perturbing effect of the jump processes of incoming species on the abundant ones.

##### 1.Multi-type critical process: a birth-death model of error catastrophe

**Authors:**Xell Brunet Guasch, P. L. Krapivsky, Tibor Antal

**Abstract:** Critical birth-death processes with $n$ distinct types are investigated. Each type $i$ cell divides independently $(i)\to(i)+(i)$ or mutates $(i)\to(i+1)$ at the same rate. The total number of cells grows exponentially as a Yule process until the maximal type $n$ cells appear, which cannot mutate but die at rate one. The last type makes the process critical and hence after the exponentially growing phase eventually all cells die with probability one. The process mimics the accumulation of mutations in a growing population where too many mutations are lethal. This has applications for understanding the mutational burden and so-called error catastrophe in cancer, bacteria, or virus. We present large-time asymptotic results for the general $n$-type critical birth-death process. We find that the mass function of the number of cells of type $k$ has algebraic and stationary tail $(\text{size})^{-1-\chi_k}$, with $\chi_k=2^{1-k}$, for $k=2,\dots,n$, in sharp contrast to the exponential tail of the first type. The same exponents describe the tail of the asymptotic survival probability $(\text{time})^{-\chi_n}$. We discuss the consequences and applications of the results for studying extinction due to mutational burden in biological populations.

##### 2.grenedalf: population genetic statistics for the next generation of pool sequencing

**Authors:**Lucas Czech, Jeffrey P. Spence, Moisés Expósito-Alonso

**Abstract:** Pool sequencing is an efficient method for capturing genome-wide allele frequencies from multiple individuals, with broad applications such as studying adaptation in Evolve-and-Resequence experiments, monitoring of genetic diversity in wild populations, and genotype-to-phenotype mapping. Here, we present grenedalf, a command line tool written in C++ that implements common population genetic statistics such as $\theta$, Tajima's D, and FST for Pool sequencing. It is orders of magnitude faster than current tools, and is focused on providing usability and scalability, while also offering a plethora of input file formats and convenience options.

##### 3.Pattern formation in a predator-prey model with Allee effect and hyperbolic mortality on networked and non-networked environments

**Authors:**Yong Ye, Jiaying Zhou

**Abstract:** With the development of network science, the Turing pattern has been proven to be formed in discrete media such as complex networks, opening up the possibility of exploring it as a generation mechanism in the context of biology, chemistry, and physics. Turing instability in the predator-prey system has been widely studied in recent years. We hope to use the predator-prey interaction relationship in biological populations to explain the influence of network topology on pattern formation. In this paper, we establish a predator-prey model with a weak Allee effect, analyze and verify the Turing instability conditions on the large ER (Erd\"{o}s-R\'{e}nyi) random network with the help of Turing stability theory and numerical experiments, and obtain the Turing instability region. The results show that the diffusion coefficient plays a decisive role in the generation of patterns, and it is interesting that the appropriate initial value will also bring beautiful patterns. When we analyze the model based on the network framework, we find that the average degree of the network has an important impact on the model, and different average degrees will lead to changes in the distribution pattern of the population.

##### 1.Comparing intervention measures in a model of a disease outbreak on a university campus

**Authors:**Alex Best, Prerna Singh

**Abstract:** A number of theoretical models have been developed in recent years modelling epidemic spread in educational settings such as universities to help inform re-opening strategies during the Covid-19 pandemic. However, these studies have had differing conclusions as to the most effective non-pharmaceutical interventions. They also largely assumed permanent acquired immunity, meaning we have less understanding of how disease dynamics will play out when immunity wanes. Here we complement these studies by developing and analysing a stochastic simulation model of disease spread on a university campus where we allow immunity to wane, expoloring the effectiveness of different interventions. We find that the two most effective interventions to limit the severity of a disease outbreak are reducing extra-household mixing and surveillance testing backed-up by a moderate isolation period. We find that contact tracing only has a limited effect, while reducing class sizes only has much effect if extra-household mixing is already low. We identify a range of measures that can not only limit an outbreak but prevent it entirely, and also comment on the variation in measures of severity that emerge from our stochastic simulations. We hope that our model may help in designing effective strategies for universities in future disease outbreaks.

##### 1.Population growth in discrete time: a renewal equation oriented survey

**Authors:**B. Boldin, O. Diekmann, J. A. J. Metz

**Abstract:** Traditionally, population models distinguish individuals on the basis of their current state. Given a distribution, a discrete time model then specifies (precisely in deterministic models, probabilistically in stochastic models) the population distribution at the next time point. The renewal equation alternative concentrates on newborn individuals and the model specifies the production of offspring as a function of age. This has two advantages: (i) as a rule, there are far fewer birth states than individual states in general, so the dimension is often low; (ii) it relates seamlessly to the next-generation matrix and the basic reproduction number. Here we start from the renewal equation for the births and use results of Feller and Thieme to characterise the asymptotic large time behaviour. Next we explicitly elaborate the relationship between the two bookkeeping schemes. This allows us to transfer the characterisation of the large time behaviour to traditional structured-population models.

##### 2.Survival of the flattest in the quasispecies model

**Authors:**Maxime Berger, Raphaël Cerf

**Abstract:** Viruses present an amazing genetic variability. An ensemble of infecting viruses, also called a viral quasispecies, is a cloud of mutants centered around a specific genotype. The simplest model of evolution, whose equilibrium state is described by the quasispecies equation, is the Moran--Kingman model. For the sharp peak landscape, we perform several exact computations and we derive several exact formulas. We obtain also an exact formula for the quasispecies distribution, involving a series and the mean fitness. A very simple formula for the mean Hamming distance is derived, which is exact and which do not require a specific asymptotic expansion (like sending the length of the macromolecules to $\infty$ or the mutation probability to $0$). We try also to extend these formulas to a general fitness landscape. We obtain an equation involving the covariance of the fitness and the Hamming class number in the quasispecies distribution. With the help of these formulas, we discuss the phenomenon of the error threshold and the notion of quasispecies. We recover the limiting quasipecies distribution in the long chain regime. We go beyond the sharp peak landscape and we consider fitness landscapes having finitely many peaks and a plateau--type landscape. We finally prove rigorously within this framework the possible occurrence of the survival of the flattest, a phenomenon which has been previously discovered by Wilke, Wang, Ofria, Lenski and Adami and which has been investigated in several works.

##### 1.Leaping through tree space: continuous phylogenetic inference for rooted and unrooted trees

**Authors:**Matthew J Penn, Neil Scheidwasser, Joseph Penn, Christl A Donnelly, David A Duchêne, Samir Bhatt

**Abstract:** Phylogenetics is now fundamental in life sciences, providing insights into the earliest branches of life and the origins and spread of epidemics. However, finding suitable phylogenies from the vast space of possible trees remains challenging. To address this problem, for the first time, we perform both tree exploration and inference in a continuous space where the computation of gradients is possible. This continuous relaxation allows for major leaps across tree space in both rooted and unrooted trees, and is less susceptible to convergence to local minima. Our approach outperforms the current best methods for inference on unrooted trees and, in simulation, accurately infers the tree and root in ultrametric cases. The approach is effective in cases of empirical data with negligible amounts of data, which we demonstrate on the phylogeny of jawed vertebrates. Indeed, only a few genes with an ultrametric signal were generally sufficient for resolving the major lineages of vertebrate. With cubic-time complexity and efficient optimisation via automatic differentiation, our method presents an effective way forwards for exploring the most difficult, data-deficient phylogenetic questions.

##### 2.Noncoding RNAs evolutionarily extend animal lifespan

**Authors:**Anyou Wang

**Abstract:** The mechanisms underlying lifespan evolution in organisms have long been mysterious. However, recent studies have demonstrated that organisms evolutionarily gain noncoding RNAs (ncRNAs) that carry endogenous profound functions in higher organisms, including lifespan. This study unveils ncRNAs as crucial drivers driving animal lifespan evolution. Species in the animal kingdom evolutionarily increase their ncRNA length in their genomes, coinciding with trimming mitochondrial genome length. This leads to lower energy consumption and ultimately lifespan extension. Notably, during lifespan extension, species exhibit a gradual acquisition of long-life ncRNA motifs while concurrently losing short-life motifs. These longevity-associated ncRNA motifs, such as GGTGCG, are particularly active in key tissues, including the endometrium, ovary, testis, and cerebral cortex. The activation of ncRNAs in the ovary and endometrium offers insights into why women generally exhibit longer lifespans than men. This groundbreaking discovery reveals the pivotal role of ncRNAs in driving lifespan evolution and provides a fundamental foundation for the study of longevity and aging.

##### 1.Branching model with state dependent offspring distribution for Chlamydia spread

**Authors:**Péter Kevei, Máté Szalai

**Abstract:** Chlamydiae are bacteria with an interesting unusual developmental cycle. A single bacterium in its infectious form (elementary body, EB) enters the host cell, where it converts into its dividing form (reticulate body, RB), and divides by binary fission. Since only the EB form is infectious, before the host cell dies, RBs start to convert into EBs. After the host cell dies RBs do not survive. We model the population growth by a 2-type discrete-time branching process, where the probability of duplication depends on the state. Maximizing the EB production leads to a stochastic optimization problem. Simulation study shows that our novel model is able to reproduce the main features of the development of the population.

##### 1.Theory for Adaptive Systems: Collective Robustness of Genotype-Phenotype Evolution

**Authors:**Tuan Minh Pham, Kunihiko Kaneko

**Abstract:** The investigation of mutually coupled dynamics, involving many degrees of freedom on two separated timescales, one for fast changes of state variables and another for the slow adaptation of parameters controlling the former's dynamics is crucial for understanding biological evolution and learning. We develop a general theory for such dynamics by extending dynamical mean field theory. We then apply our framework to biological systems whose fate is determined by the evolution of genotype-phenotype relationship. Here phenotypic evolution is shaped by stochastic gene-expression fast dynamics and is coupled to selection-based slow changes of genotypes encoding the network of gene regulations. We find dynamically robust patterns of phenotypes can be achieved under an intermediate level of external noise where the genotype-phenotype relation evolves in such a way that results in intrinsic out-of-equilibrium fluctuations of phenotypes even in the absence of that noise.

##### 1.Muller's ratchet in a near-critical regime: tournament versus fitness proportional selection

**Authors:**Jan Lukas Igelbrink, Adrián González Casanova, Charline Smadi, Anton Wakolbinger

**Abstract:** Muller's ratchet, in its prototype version, models a haploid, asexual population whose size~$N$ is constant over the generations. Slightly deleterious mutations are acquired along the lineages at a constant rate, and individuals carrying less mutations have a selective advantage. The classical variant considers {\it fitness proportional} selection, but other fitness schemes are conceivable as well. Inspired by the work of Etheridge et al. ([EPW09]) we propose a parameter scaling which fits well to the ``near-critical'' regime that was in the focus of [EPW09] (and in which the mutation-selection ratio diverges logarithmically as $N\to \infty$). Using a Moran model, we investigate the``rule of thumb'' given in [EPW09] for the click rate of the ``classical ratchet'' by putting it into the context of new results on the long-time evolution of the size of the best class of the ratchet with (binary) tournament selection, which (other than that of the classical ratchet) follows an autonomous dynamics up to the time of its extinction. In [GSW23] it was discovered that the tournament ratchet has a hierarchy of dual processes which can be constructed on top of an Ancestral Selection graph with a Poisson decoration. For a regime in which the mutation/selection-ratio remains bounded away from 1, this was used in [GSW23] to reveal the asymptotics of the click rates as well as that of the type frequency profile between clicks. We will describe how these ideas can be extended to the near-critical regime in which the mutation-selection ratio of the tournament ratchet converges to 1 as $N\to \infty$.

##### 2.Digital contact tracing/notification for SARS-CoV-2: a retrospective of what went wrong

**Authors:**Joanna Masel, James Petrie, Jason Bay, Wolfgang Ebbers, Aalekh Sharan, Scott Leibrand, Andreas Gebhard, Samuel Zimmerman

**Abstract:** Digital contact tracing/notification was initially hailed as a promising strategy to combat SARS-CoV-2, but in most jurisdictions it did not live up to its promise. To avert a given transmission event, both parties must have adopted the tech, it must detect the contact, the primary case must be promptly diagnosed, notifications must be triggered, and the secondary case must change their behavior to avoid the focal tertiary transmission event. Achieving a 26% reduction in R(t) requires 80% success rates at each of these six points of failure. Here we review the six failure rates experienced by a variety of digital contact tracing/notification schemes, including Singapore's TraceTogether, India's Aarogya Setu, and leading implementations of the Google Apple Exposure Notification system. This leads to a number of recommendations, e.g. that tracing/notification apps be multi-functional and integrated with testing, manual contact tracing, and the gathering of critical scientific data, and that the narrative be framed in terms of user autonomy rather than user privacy.

##### 1.Wind turbine power and land cover effects on cumulative bat deaths

**Authors:**Aristides Moustakas, Panagiotis Georgiakakis, Elzbieta Kret, Eleftherios Kapsalis

**Abstract:** Wind turbines (WT) cause bird and bat mortalities which depend on the WT and landscape features. The effects of WT features and environmental variables at different spatial scales associated to bat deaths in a mountainous and forested area in Thrace, NE Greece were investigated. Initially, we sought to quantify the most lethal WT characteristic between tower height, rotor diameter and power. The scale of interaction distance between bat deaths and the land cover characteristics surrounding the WTs was quantified. A statistical model was trained and validated against bat deaths and WT, land cover and topography features. Variance partitioning between bat deaths and the explanatory covariates was conducted. The trained model was used to predict bat deaths attributed to existing and future wind farm development in the region. Results indicated that the optimal interaction distance between WT and surrounding land cover was 5 km, the larger distance than the ones examined. WT power, natural land cover type and distance from water explained 40 %, 15 % and 11 % respectively of the total variance in bat deaths by WTs. The model predicted that operating but not surveyed WTs comprise of 377.8% and licensed but not operating yet will contribute to 210.2% additional deaths than the ones recorded. Results indicate that among all WT features and land cover characteristics, wind turbine power is the most significant factor associated to bat deaths. Results indicated that WTs located within 5 km buffer comprised of natural land cover types have substantial higher deaths. More WT power will result in more deaths. Wind turbines should not be licensed in areas where natural land cover at a radius of 5km exceeds 50%. These results are discussed in the climate-land use-biodiversity-energy nexus.

##### 2.Steady-state analysis of networked epidemic models

**Authors:**Sei Zhen Khong, Lanlan Su

**Abstract:** Compartmental epidemic models with dynamics that evolve over a graph network have gained considerable importance in recent years but analysis of these models is in general difficult due to their complexity. In this paper, we develop two positive feedback frameworks that are applicable to the study of steady-state values in a wide range of compartmental epidemic models, including both group and networked processes. In the case of a group (resp. networked) model, we show that the convergence limit of the susceptible proportion of the population (resp. the susceptible proportion in at least one of the subgroups) is upper bounded by the reciprocal of the basic reproduction number (BRN) of the model. The BRN, when it is greater than unity, thus demonstrates the level of penetration into a subpopulation by the disease. Both non-strict and strict bounds on the convergence limits are derived and shown to correspond to substantially distinct scenarios in the epidemic processes, one in the presence of the endemic state and another without. Formulae for calculating the limits are provided in the latter case. We apply the developed framework to examining various group and networked epidemic models commonly seen in the literature to verify the validity of our conclusions.

##### 3.Closed ecosystems extract energy through self-organized nutrient cycles

**Authors:**Akshit Goyal, Avi I. Flamholz, Alexander P. Petroff, Arvind Murugan

**Abstract:** Our planet is roughly closed to matter, but open to energy input from the sun. However, to harness this energy, organisms must transform matter from one chemical (redox) state to another. For example, photosynthetic organisms can capture light energy by carrying out a pair of electron donor and acceptor transformations (e.g., water to oxygen, CO$_2$ to organic carbon). Closure of ecosystems to matter requires that all such transformations are ultimately balanced, i.e., other organisms must carry out corresponding reverse transformations, resulting in cycles that are coupled to each other. A sustainable closed ecosystem thus requires self-organized cycles of matter, in which every transformation has sufficient thermodynamic favorability to maintain an adequate number of organisms carrying out that process. Here, we propose a new conceptual model that explains the self-organization and emergent features of closed ecosystems. We study this model with varying levels of metabolic diversity and energy input, finding that several thermodynamic features converge across ecosystems. Specifically, irrespective of their species composition, large and metabolically diverse communities self-organize to extract roughly 10% of the maximum extractable energy, or 100 fold more than randomized communities. Moreover, distinct communities implement energy extraction in convergent ways, as indicated by strongly correlated fluxes through nutrient cycles. As the driving force from light increases, however, these features -- fluxes and total energy extraction -- become more variable across communities, indicating that energy limitation imposes tight thermodynamic constraints on collective metabolism.

##### 4.Species interactions reproduce abundance correlations patterns in microbial communities

**Authors:**José Camacho-Mateu, Aniello Lampo, Matteo Sireci, Miguel Ángel Muñoz, José A. Cuesta

**Abstract:** During the last decades macroecology has identified broad-scale patterns of abundances and diversity of microbial communities and put forward some potential explanations for them. However, these advances are not paralleled by a full understanding of the dynamical processes behind them. In particular, abundance fluctuations over metagenomic samples are found to be correlated, but reproducing populations through appropriate population models remains still an open task. The present paper tackles this problem and points to species interactions as a necessary mechanism to account for them. Specifically, we discuss several possibilities to include interactions in population models and recognize Lotka-Volterra constants as successful ansatz. We design a Bayesian inference algorithm to obtain sets of interaction constants able to reproduce the experimental correlation distributions much better than the state-of-the-art attempts. Importantly, the model still reproduces single-species, experimental, macroecological patterns previously detected in the literature, concerning the abundance fluctuations across both species and communities. Endorsed by the agreement with the observed phenomenology, our analysis provides insights on the properties of microbial interactions, and suggests their sparsity as a necessary feature to balance the emergence of different patterns.

##### 1.Scaling symmetries and parameter reduction in epidemic SI(R)S models

**Authors:**Florian Nill

**Abstract:** Symmetry concepts in parametrized dynamical systems may reduce the number of external parameters by a suitable normalization prescription. If, under the action of a symmetry group G, parameter space A becomes a (locally) trivial principal bundle, A ~ A/G x G, then the normalized dynamics only depends on the quotient A/G. In this way, the dynamics of fractional variables in homogeneous epidemic SI(R)S models, with standard incidence, absence of R-susceptibility and compartment independent birth and death rates, turns out to be isomorphic to (a marginally extended version of) Hethcote's classic endemic model, first presented in 1973. The paper studies a 10-parameter master model with constant and I-linear vaccination rates, vertical transmission and a vaccination rate for susceptible newborns. As recently shown by the author, all demographic parameters are redundant. After adjusting time scale, the remaining 5-parameter model admits a 3-dimensional abelian scaling symmetry. By normalization we end up with Hethcote's extended 2-parameter model. Thus, in view of symmetry concepts, reproving theorems on endemic bifurcation and stability in such models becomes needless.

##### 1.Fractional model of COVID--19 with pathogens as shedding effects

**Authors:**Faïçal Ndaïrou, Moein Khalighi, Leo Lahti

**Abstract:** To develop effective strategies for controlling the spread of the virus and potential future outbreaks, a deep understanding of disease transmission dynamics is crucial. This study proposes a modification to existing mathematical models used to describe the transmission dynamics of COVID-19 with environmental pathogens, incorporating a variable population, and employing incommensurate fractional order derivatives in ordinary differential equations. Our analysis accurately computes the basic reproduction number and demonstrates the global stability of the disease-free equilibrium point. Numerical simulations fitted to real data from South Africa show the efficacy of our proposed model, with fractional models enhancing flexibility. We also provide reliable values for initial conditions, model parameters, and order derivatives, and examine the sensitivity of model parameters. Our study provides valuable insights into COVID-19 transmission dynamics and has the potential to inform the development of effective control measures and prevention strategies.

##### 2.Image background assessment as a novel technique for insect microhabitat identification

**Authors:**Sesa Singha Roy, Reid Tingley, Alan Dorin

**Abstract:** The effects of climate change, urbanisation and agriculture are changing the way insects occupy habitats. Some species may utilise anthropogenic microhabitat features for their existence, either because they prefer them to natural features, or because of no choice. Other species are dependent on natural microhabitats. Identifying and analysing these insects' use of natural and anthropogenic microhabitats is important to assess their responses to a changing environment, for improving pollination and managing invasive pests. Traditional studies of insect microhabitat use can now be supplemented by machine learning-based insect image analysis. Typically, research has focused on automatic insect classification, but valuable data in image backgrounds has been ignored. In this research, we analysed the image backgrounds available on the ALA database to determine their microhabitats. We analysed the microhabitats of three insect species common across Australia: Drone flies, European honeybees and European wasps. Image backgrounds were classified as natural or anthropogenic microhabitats using computer vision and machine learning tools benchmarked against a manual classification algorithm. We found flies and honeybees in natural microhabitats, confirming their need for natural havens within cities. Wasps were commonly seen in anthropogenic microhabitats. Results show these insects are well adapted to survive in cities. Management of this invasive pest requires a thoughtful reduction of their access to human-provided resources. The assessment of insect image backgrounds is instructive to document the use of microhabitats by insects. The method offers insight that is increasingly vital for biodiversity management as urbanisation continues to encroach on natural ecosystems and we must consciously provide resources within built environments to maintain insect biodiversity and manage invasive pests.

##### 1.Information encoded in gene-frequency trajectories

**Authors:**Konstantinos Mavreas, David Waxman

**Abstract:** In this work we present a systematic mathematical approximation scheme that exposes the way that information, about the evolutionary forces of selection and random genetic drift, is encoded in gene-frequency trajectories. We determine approximate, time-dependent, gene-frequency trajectory statistics, assuming additive selection. We use the probability of fixation to test and illustrate the approximation scheme introduced. For the case where the strength of selection and the effective population size have constant values, we show how a standard result for the probability of fixation, under the diffusion approximation, systematically emerges, when increasing numbers of approximate trajectory statistics are taken into account. We then provide examples of how time-dependent parameters influence gene-frequency statistics.

##### 1.A Markov chain model to investigate the spread of antibiotic-resistant bacteria in hospitals

**Authors:**Fabio A. C. C. Chalub, Antonio Gómez-Corral, Martín López-García, Fátima Palacios-Rodríguez

**Abstract:** This paper proposes a Markov chain model to describe the spread of a single bacterial species in a hospital ward where patients may be free of bacteria or may carry bacterial strains that are either sensitive or resistant to antimicrobial agents. The aim is to determine the probability law of the exact reproduction number Rexact,0 which is here defined as the random number of secondary infections generated by those patients who are accommodated in a predetermined bed before a patient who is free of bacteria is accommodated in this bed for the first time. Specifically, we decompose the exact reproduction number Rexact,0 into two contributions allowing us to distinguish between infections due to the sensitive and the resistant bacterial strains. Our methodology is mainly based on structured Markov chains and the use of related matrix-analytic methods.

##### 1.Dynamics of niche construction in adaptable populations evolving in diverse environments

**Authors:**Eleni Nisioti, Clément Moulin-Frier

**Abstract:** In both natural and artificial studies, evolution is often seen as synonymous to natural selection. Individuals evolve under pressures set by environments that are either reset or do not carry over significant changes from previous generations. Thus, niche construction (NC), the reciprocal process to natural selection where individuals incur inheritable changes to their environment, is ignored. Arguably due to this lack of study, the dynamics of NC are today little understood, especially in real-world settings. In this work, we study NC in simulation environments that consist of multiple, diverse niches and populations that evolve their plasticity, evolvability and niche-constructing behaviors. Our empirical analysis reveals many interesting dynamics, with populations experiencing mass extinctions, arms races and oscillations. To understand these behaviors, we analyze the interaction between NC and adaptability and the effect of NC on the population's genomic diversity and dispersal, observing that NC diversifies niches. Our study suggests that complexifying the simulation environments studying NC, by considering multiple and diverse niches, is necessary for understanding its dynamics and can lend testable hypotheses to future studies of both natural and artificial systems.

##### 1.Spatial patterns and biodiversity in rock-paper-scissors models with regional unevenness

**Authors:**J. Menezes, M. Tenorio

**Abstract:** Climate changes may affect ecosystems destabilising relationships among species. We investigate the spatial rock-paper-scissors models with a regional unevenness that reduces the selection capacity of organisms of one species. Our results show that the regionally weak species predominates in the local ecosystem, while spiral patterns appear far from the region, where individuals of every species play the rock-paper-scissors game with the same strength. Because the weak species controls all local territory, it is attractive for the other species to enter the local ecosystem to conquer the territory. However, our stochastic simulations show that the transitory waves formed when organisms of the strong species reach the region are quickly destroyed because of local strength unbalance in the selection game rules. Computing the effect of the topology on population dynamics, we find that the prevalence of the weak species becomes more significant if the transition of the selection capacity to the area of uneven rock-paper-scissors rules is smooth. Finally, our findings show that the biodiversity loss due to the arising of regional unevenness is minimised if the transition to the region where the cyclic game is unbalanced is abrupt. Our results may be helpful to biologists in comprehending the consequences of changes in the environmental conditions on species coexistence and spatial patterns in complex systems.

##### 1.Modelling disease impact: lifespan reduction is greatest for young adults in an exogenous damage model of disease

**Authors:**Rebecca Tobin, Glen Pridham, Andrew D. Rutenberg

**Abstract:** We model the effects of disease and other exogenous damage during human aging. While the exogenous damage is repaired at the end of acute disease, propagated secondary damage remains. We consider both short-term mortality effects due to (acute) exogenous damage and long-term mortality effects due to propagated damage within the context of a generic network model (GNM) of individual aging. Across a wide range of disease durations and severities we find that while excess short-term mortality is highest for the oldest individuals, the long-term years of life lost are highest for the youngest individuals. These appear to be universal effects of human disease. We support this conclusion with a phenomenological model coupling damage and mortality. Our results are qualitatively consistent with existing observational studies, though these are mostly limited to short time-horizons. Short-time horizon studies may have significant limitations for understanding the lifetime impacts of disease on both individuals and populations.

##### 1.A Chip-Firing Game for Biocrust Reverse Succession

**Authors:**Shloka V. Janapaty

**Abstract:** Experimental work suggests that biological soil crusts, dominant primary producers in drylands and tundra, are particularly vulnerable to disturbances that cause reverse ecological succession. To model successional transitions in biocrust communities, we propose a resource-firing game that captures succession dynamics without specifying detailed function forms. The model is evaluated in idealized terrestrial ecosystems, where disturbances are modeled as a reduction in available resources that triggers inter-species competition. The resource-firing game is executed on a finite graph with nodes representing species in the community and a sink node that becomes active when every species is depleted of resources. First, we discuss the theoretical basis of the resource-firing game, evaluate it in the light of existing literature, and consider the characteristics of a biocrust community that has evolved to equilibrium. We then examine the dependence of resource-firing and game stability on species richness, showing that high species richness increases the probability of very short and long avalanches, but not those of intermediate length. Indeed, this result suggests that the response of the community to disturbance is both directional and episodic, proceeding towards reverse succession in bursts of variable length. Finally, we incorporate the spatial structure of the biocrust community into a Cayley Tree and derive a formula for the probability that a disturbance, modeled as a random attack, initiates a large species-death event.

##### 2.Cell lineage statistics with incomplete population trees

**Authors:**Arthur Genthon, Takashi Nozoe, Luca Peliti, David Lacoste

**Abstract:** Cell lineage statistics is a powerful tool for inferring cellular parameters, such as division rate, death rate or the population growth rate. Yet, in practice such an analysis suffers from a basic problem: how should we treat incomplete lineages that do not survive until the end of the experiment? Here, we develop a model-independent theoretical framework to address this issue. We show how to quantify fitness landscape, survivor bias and selection for arbitrary cell traits from cell lineage statistics in the presence of death, and we test this method using an experimental data set in which a cell population is exposed to a drug that kills a large fraction of the population. This analysis reveals that failing to properly account for dead lineages can lead to misleading fitness estimations. For simple trait dynamics, we prove and illustrate numerically that the fitness landscape and the survivor bias can in addition be used for the non-parametric estimation of the division and death rates, using only lineage histories. Our framework provides universal bounds on the population growth rate, and a fluctuation-response relation which quantifies the reduction of population growth rate due to the variability in death rate. Further, in the context of cell size control, we obtain generalizations of Powell's relation that link the distributions of generation times with the population growth rate, and show that the survivor bias can sometimes conceal the adder property, namely the constant increment of volume between birth and division.

##### 1.Biophysical Cybernetics of Directed Evolution and Eco-evolutionary Dynamics

**Authors:**Bryce Allen Bagley

**Abstract:** Many major questions in the theory of evolutionary dynamics can in a meaningful sense be mapped to analyses of stochastic trajectories in game theoretic contexts. Often the approach is to analyze small numbers of distinct populations and/or to assume dynamics occur within a regime of population sizes large enough that deterministic trajectories are an excellent approximation of reality. The addition of ecological factors, termed "eco-evolutionary dynamics", further complicates the dynamics and results in many problems which are intractable or impractically messy for current theoretical methods. However, an analogous but underexplored approach is to analyze these systems with an eye primarily towards uncertainty in the models themselves. In the language of researchers in Reinforcement Learning and adjacent fields, a Partially Observable Markov Process. Here we introduce a duality which maps the complexity of accounting for both ecology and individual genotypic/phenotypic types onto a problem of accounting solely for underlying information-theoretic computations rather than drawing physical boundaries which do not change the computations. Armed with this equivalence between computation and the relevant biophysics, which we term Taak-duality, we attack the problem of "directed evolution" in the form of a Partially Observable Markov Decision Process. This provides a tractable case of studying eco-evolutionary trajectories of a highly general type, and of analyzing questions of potential limits on the efficiency of evolution in the directed case.

##### 1.The Role of Quarantine and Isolation in Controlling COVID-19 Hospitalization in Oman

**Authors:**Maryam Al-Yahyai
Department of Mathematics, College of Science, Sultan Qaboos University, Muscat, Oman, Fatma Al-Musalhi
Department of Mathematics, College of Science, Sultan Qaboos University, Muscat, Oman, Nasser Al-Salti
Department of Applied Mathematics and Science, National University of Science and Technology, Muscat, Oman, Ibrahim Elmojtaba
Department of Mathematics, College of Science, Sultan Qaboos University, Muscat, Oman

**Abstract:** In this paper, we build a mathematical model for the dynamics of COVID-19 to assess the impact of placing healthy individuals in quarantine and isolating infected ones on the number of hospitalization and intensive care unit cases. The proposed model is fully analyzed in order to prove the positivity of solutions, to study the local and global stability of the disease-free equilibria and to drive the basic and control reproduction numbers of the model. Oman COVID-19 data is used to calibrate the model and estimate the parameters. In particular, the published data for the year 2020 is used, when two waves of the disease hit the country. Moreover, this period of time is chosen when no vaccine had been introduced, but only the non-pharmaceutical intervention (NPI) strategies were the only effective methods to control the spread and, consequently, control the hospitalization cases to avoid pressuring the health system. Based on the estimated parameters, the reproduction number and contribution of different transmission routes are approximated numerically. Sensitivity analysis is performed to identify the significant parameters in spreading the disease. Numerical simulation is carried out to demonstrate the effects of quarantine and isolation on the number of hospitalized cases.

##### 1.Multi-Species Prey-Predator Dynamics During a Multi-Strain Pandemic

**Authors:**Ariel Alexi, Ariel Rosenfeld, Teddy Lazebnik

**Abstract:** Small and large scale pandemics are a natural phenomenon repeatably appearing throughout history, causing ecological and biological shifts in ecosystems and a wide range of their habitats. These pandemics usually start with a single strain but shortly become multi-strain due to a mutation process of the pathogen causing the epidemic. In this study, we propose a novel eco-epidemiological model that captures multi-species prey-predator dynamics with a multi-strain pandemic. The proposed model extends and combines the Lotka-Volterra prey-predator model and the Susceptible-Infectious-Recovered (SIR) epidemiological model. We investigate the ecosystem's sensitivity and stability during such a multi-strain pandemic through extensive simulation relying on both synthetic cases as well as two real-world configurations. Our results are aligned with known ecological and epidemiological findings, thus supporting the adequacy of the proposed model in realistically capturing the complex eco-epidemiological properties of the multi-species multi-strain pandemic dynamics.

##### 1.Directionality Theory and the Origin of Life

**Authors:**Lloyd Demetrius

**Abstract:** The origin of cellular life can be described in terms of the transition from inorganic matter: solids, liquids and gases, to the emergence of cooperative assemblies of organic matter, DNA and proteins,capable of replication and metabolism. Directionality Theory is a mathematical model of the collective behavior of populations of organic matter: cells and higher organisms. Evolutionary entropy, the cornerstone of the theory, is a statistical measure of the cooperativity of the interacting components that comprise the population. The main tenet of Directionality Theory is the Entropic Principle of Collective Behavior: The collective behavior of aggregates of organic matter is contingent on the population size and the external energy source, and characterized by extremal states of evolutionary entropy. This article invokes Directionality Theory to provide an evolutionary rationale for the following sequence of transformations which define the emergence of cellular life: 1. The self-assembly of activated macromolecules from inorganic matter 2. The emergence of an RNA world, defined by RNA molecules with catalytic and replicative properties 3. The origin of cellular life, the integration of the three carbon-based polymers: DNA, proteins and lipids, to generate a metabolic and replicative unit.

##### 1.Phylo2Vec: a vector representation for binary trees

**Authors:**Matthew J Penn, Neil Scheidwasser, Mark P Khurana, David A Duchêne, Christl A Donnelly, Samir Bhatt

**Abstract:** Binary phylogenetic trees inferred from biological data are central to understanding the shared evolutionary history of organisms. Inferring the placement of latent nodes in a tree by any optimality criterion (e.g., maximum likelihood) is an NP-hard problem, propelling the development of myriad heuristic approaches. Yet, these heuristics often lack a systematic means of uniformly sampling random trees or effectively exploring a tree space that grows factorially, which are crucial to optimisation problems such as machine learning. Accordingly, we present Phylo2Vec, a new parsimonious representation of a phylogenetic tree. Phylo2Vec maps any binary tree with $n$ leaves to an integer vector of length $n$. We prove that Phylo2Vec is both well-defined and bijective to the space of phylogenetic trees. The advantages of Phylo2Vec are twofold: i) easy uniform sampling of binary trees and ii) systematic ability to traverse tree space in very large or small jumps. As a proof of concept, we use Phylo2Vec for maximum likelihood inference on five real-world datasets and show that a simple hill climbing-based optimisation efficiently traverses the vastness of tree space from a random to an optimal tree.

##### 2.Revising the global biogeography of plant life cycles

**Authors:**Tyler Poppenwimer, Itay Mayrose, Niv DeMalach

**Abstract:** There are two main life cycles in plants, annual and perennial. These life cycles are associated with different traits, which determine ecosystem function. Although life cycles are textbook examples of plant adaptation to different environments, we lack comprehensive knowledge regarding global distributional patterns. Here, we assembled an extensive database of plant life cycle assignments of 235,000 plant species coupled with millions of georeferenced datapoints to map the worldwide biogeography of life cycles. We found that annuals are half as common as initially thought, accounting for only 6% of species. Our analyses indicate annuals are favored in hot and dry regions. However, a more accurate model shows annual species' prevalence is driven by temperature and precipitation in the driest quarter (rather than yearly means), explaining, for example, why some Mediterranean systems have more annuals than deserts. Furthermore, this pattern remains consistent among different families, indicating convergent evolution. Finally, we demonstrate that increasing climate variability and anthropogenic disturbance increase annual favorability. Considering future climate change, we predict an increase in annual prevalence for 81% of the world's ecoregions by 2100. Overall, our analyses raise concerns for ecosystem services provided by perennials as ongoing changes are leading to a more annuals-dominated world.

##### 1.The Theory of Gene Family Histories

**Authors:**Marc Hellmuth, Peter F. Stadler

**Abstract:** Most genes are part of larger families of evolutionary related genes. The history of gene families typically involves duplications and losses of genes as well as horizontal transfers into other organisms. The reconstruction of detailed gene family histories, i.e., the precise dating of evolutionary events relative to phylogenetic tree of the underlying species has remained a challenging topic despite their importance as a basis for detailed investigations into adaptation and functional evolution of individual members of the gene family. The identification of orthologs, moreover, is a particularly important subproblem of the more general setting considered here. In the last few years, an extensive body of mathematical results has appeared that tightly links orthology, a formal notion of best matches among genes, and horizontal gene transfer. The purpose of this chapter is the broadly outline some of the key mathematical insights and to discuss their implication for practical applications. In particular, we focus on tree-free methods, i.e., methods to infer orthology or horizontal gene transfer as well as gene trees, species trees and reconciliations between them without using \emph{a priori} knowledge of the underlying trees or statistical models for the inference of phylogenetic trees. Instead, the initial step aims to extract binary relations among genes.

##### 2.Reporting delays: a widely neglected impact factor in COVID-19 forecasts

**Authors:**Long MA, Piet Van Mieghem, Maksim Kitsak

**Abstract:** Epidemic forecasts are only as good as the accuracy of epidemic measurements. Is epidemic data, particularly COVID-19 epidemic data, clean and devoid of noise? Common sense implies the negative answer. While we cannot evaluate the cleanliness of the COVID-19 epidemic data in a holistic fashion, we can assess the data for the presence of reporting delays. In our work, through the analysis of the first COVID-19 wave, we find substantial reporting delays in the published epidemic data. Motivated by the desire to enhance epidemic forecasts, we develop a statistical framework to detect, uncover, and remove reporting delays in the infectious, recovered, and deceased epidemic time series. Our framework can uncover and analyze reporting delays in 8 regions significantly affected by the first COVID-19 wave. Further, we demonstrate that removing reporting delays from epidemic data using our statistical framework may decrease the error in epidemic forecasts. While our statistical framework can be used in combination with any epidemic forecast method that intakes infectious, recovered, and deceased data, to make a basic assessment, we employed the classical SIRD epidemic model. Our results indicate that the removal of reporting delays from the epidemic data may decrease the forecast error by up to 50. We anticipate that our framework will be indispensable in the analysis of novel COVID-19 strains and other existing or novel infectious diseases.

##### 1.Evolutionary stability of antigenically escaping viruses

**Authors:**Victor Chardès, Andrea Mazzolini, Thierry Mora, Aleksandra M. Walczak

**Abstract:** Antigenic variation is the main immune escape mechanism for RNA viruses like influenza or SARS-CoV-2. While high mutation rates promote antigenic escape, they also induce large mutational loads and reduced fitness. It remains unclear how this cost-benefit trade-off selects the mutation rate of viruses. Using a traveling wave model for the co-evolution of viruses and host immune systems in a finite population, we investigate how immunity affects the evolution of the mutation rate and other non-antigenic traits, such as virulence. We first show that the nature of the wave depends on how cross-reactive immune systems are, reconciling previous approaches. The immune-virus system behaves like a Fisher wave at low cross-reactivities, and like a fitness wave at high cross-reactivities. These regimes predict different outcomes for the evolution of non-antigenic traits. At low cross-reactivities, the evolutionarily stable strategy is to maximize the speed of the wave, implying a higher mutation rate and increased virulence. At large cross-reactivities, where our estimates place H3N2 influenza, the stable strategy is to increase the basic reproductive number, keeping the mutation rate to a minimum and virulence low.

##### 1.A discrete model for the growth and spread of the Scottish populations of red squirrels (Sciurus vulgaris) and grey squirrels (Sciurus carolinensis)

**Authors:**Jean-Baptiste Gramain

**Abstract:** In this article, a model, discrete in space and time, is developed to describe the growth and spread of the Scottish populations of red squirrels (Sciurus vulgaris) and grey squirrel (Sciurus carolinensis). The initial state for the model is designed using a large dataset of records of sightings of individuals of both species reported by members of the public. Choices of parameters involved in the model and their values are informed by the analysis of this dataset for the period 2011-2016, and model predictions are compared to records for the years 2006-2019.

##### 1.Exact solutions for diffusive transport on heterogeneous growing domains

**Authors:**Stuart T. Johnston, Matthew J. Simpson

**Abstract:** From the smallest biological systems to the largest cosmological structures, spatial domains undergo expansion and contraction. Within these growing domains, diffusive transport is a common phenomenon. Mathematical models have been widely employed to investigate diffusive processes on growing domains. However, a standard assumption is that the domain growth is spatially uniform. There are many relevant examples where this is not the case, such as the colonisation of growing gut tissue by neural crest cells. As such, it is not straightforward to disentangle the individual roles of heterogeneous growth and diffusive transport. Here we present exact solutions to models of diffusive transport on domains undergoing spatially non-uniform growth. The exact solutions are obtained via a combination of transformation, convolution and superposition techniques. We verify the accuracy of these solutions via comparison with simulations of a corresponding lattice-based random walk. We explore various domain growth functions, including linear growth, exponential growth and contraction, and oscillatory growth. Provided the domain size remains positive, we find that the derived solutions are valid. The exact solutions reveal the relationship between model parameters, such as the diffusivity and the type and rate of domain growth, and key statistics, such as the survival and splitting probabilities.

##### 2.A model for seagrass species competition: dynamics of the symmetric case

**Authors:**Pablo Moreno-Spiegelberg, Damià Gomila

**Abstract:** We propose a general population dynamics model for two seagrass species growing and interacting in two spatial dimensions. The model includes spatial terms accounting for the clonal growth characteristics of seagrasses, and coupling between species through the net mortality rate. We consider both intraspecies and interspecies facilitative and competitive interactions, allowing density-dependent interaction mechanisms. Here we study the case of very similar species with reciprocal interactions, which allows reducing the number of the model parameters to just four, and whose bifurcation structure can be considered the backbone of the complete system. We find that the parameter space can be divided into ten regions with qualitatively different bifurcation diagrams. These regimes can be further grouped into just five regimes with different ecological interpretations. Our analysis allows the classifying of all possible density distributions and dynamical behaviors of meadows with two coexisting species.

##### 3.Network topology and movement cost, not updating mechanism, determine the evolution of cooperation in mobile structured populations

**Authors:**Diogo L. Pires, Igor Erovenko, Mark Broom

**Abstract:** Evolutionary models are used to study the self-organisation of collective action, often incorporating population structure due to its ubiquitous presence and long-known impact on emerging phenomena. We investigate the evolution of multiplayer cooperation in mobile structured populations, where individuals move strategically on networks and interact with those they meet in groups of variable size. We find that the evolution of multiplayer cooperation primarily depends on the network topology and movement cost while using different stochastic update rules seldom influences evolutionary outcomes. Cooperation robustly co-evolves with movement on complete networks and structure has a partially detrimental effect on it. These findings contrast an established wisdom in evolutionary graph theory that cooperation can only emerge under some update rules and if the average degree is low. We find that group-dependent movement erases the locality of interactions, suppresses the impact of evolutionary structural viscosity on the fitness of individuals, and leads to assortative behaviour that is much more powerful than viscosity in promoting cooperation. We analyse the differences remaining between update rules through a comparison of evolutionary outcomes and fixation probabilities.

##### 1.Playing it safe: information constrains collective betting strategies

**Authors:**Philipp Fleig, Vijay Balasubramanian

**Abstract:** Every interaction of a living organism with its environment involves the placement of a bet. Armed with partial knowledge about a stochastic world, the organism must decide its next step or near-term strategy, an act that implicitly or explicitly involves the assumption of a model of the world. Better information about environmental statistics can improve the bet quality, but in practice resources for information gathering are always limited. We argue that theories of optimal inference dictate that ``complex'' models are harder to infer with bounded information and lead to larger prediction errors. Thus, we propose a principle of ``playing it safe'' where, given finite information gathering capacity, biological systems should be biased towards simpler models of the world, and thereby to less risky betting strategies. In the framework of Bayesian inference, we show that there is an optimally safe adaptation strategy determined by the Bayesian prior. We then demonstrate that, in the context of stochastic phenotypic switching by bacteria, implementation of our principle of ``playing it safe'' increases fitness (population growth rate) of the bacterial collective. We suggest that the principle applies broadly to problems of adaptation, learning and evolution, and illuminates the types of environments in which organisms are able to thrive.

##### 2.Robustness and complexity

**Authors:**Steven A. Frank

**Abstract:** When a biological system robustly corrects component-level errors, the direct pressure on component performance declines. Components may become less reliable, maintain more genetic variability, or drift neutrally in design, creating the basis for new forms of organismal complexity. This article links the protection-decay dynamic to other aspects of robust and complex systems. Examples include the hourglass pattern of biological development and Doyle's hourglass architecture for robustly complex systems in engineering. The deeply and densely connected wiring architecture in biology's cellular controls and in machine learning's computational neural networks provide another link. By unifying these seemingly different aspects into a unified framework, we gain a new perspective on robust and complex systems.

##### 1.Back to the future: a simplified and intuitive derivation of the Lotka-Euler equation

**Authors:**Carlos Hernandez-Suarez

**Abstract:** The Lotka-Euler equation is a mathematical expression used to study population dynamics and growth, particularly in the context of demography and ecology. The growth rate $\lambda$ is the speed at which $N$ individuals produce their offspring, resulting in a population size of $N R_0$, where $R_0$ is the average offspring size. It is essentially a birth process, and here it is shown that by reversing the process to a death process, in which $N R_0$ individuals die at a rate $\lambda^{-1}$, the derivation of the Lotka-Euler equation becomes more intuitive and direct, both in discrete and continuous time.

##### 1.Bayesian mixture models for phylogenetic source attribution from consensus sequences and time since infection estimates

**Authors:**Alexandra Blenkinsop, Lysandros Sofocleous, Francesco di Lauro, Evangelia Georgia Kostaki, Ard van Sighem, Daniela Bezemer, Thijs van de Laar, Peter Reiss, Godelieve de Bree, Nikos Pantazis, Oliver Ratmann

**Abstract:** In stopping the spread of infectious diseases, pathogen genomic data can be used to reconstruct transmission events and characterize population-level sources of infection. Most approaches for identifying transmission pairs do not account for the time that passed since divergence of pathogen variants in individuals, which is problematic in viruses with high within-host evolutionary rates. This is prompting us to consider possible transmission pairs in terms of phylogenetic data and additional estimates of time since infection derived from clinical biomarkers. We develop Bayesian mixture models with an evolutionary clock as signal component and additional mixed effects or covariate random functions describing the mixing weights to classify potential pairs into likely and unlikely transmission pairs. We demonstrate that although sources cannot be identified at the individual level with certainty, even with the additional data on time elapsed, inferences into the population-level sources of transmission are possible, and more accurate than using only phylogenetic data without time since infection estimates. We apply the approach to estimate age-specific sources of HIV infection in Amsterdam MSM transmission networks between 2010-2021. This study demonstrates that infection time estimates provide informative data to characterize transmission sources, and shows how phylogenetic source attribution can then be done with multi-dimensional mixture models.

##### 2.Fire responses shape plant communities in a minimal model for fire ecosystems across the world

**Authors:**Marta Magnani, Rubén Díaz-Sierra, Luke Sweeney, Antonello Provenzale, Mara Baudena

**Abstract:** Across plant communities worldwide, fire regimes reflect a combination of climatic factors and plant characteristics. To shed new light on the complex relationships between plant characteristics and fire regimes, we developed a new conceptual, mechanistic model that includes plant competition, stochastic fires, and fire-vegetation feedback. Considering a single standing plant functional type, we observed that highly flammable and slowly colonizing plants can persist only when they have a strong fire response, while fast colonizing and less flammable plants can display a larger range of fire responses. At the community level, the fire response of the strongest competitor determines the existence of alternative ecological states, i.e. different plant communities, under the same environmental conditions. Specifically, when the strongest competitor had a very strong fire response, such as in Mediterranean forests, only one ecological state could be achieved. Conversely, when the strongest competitor was poorly fire-adapted, alternative ecological states emerged, for example between tropical humid savannas and forests, or between different types of boreal forests. These findings underline the importance of including the plant fire response when modeling fire ecosystems, e.g. to predict the vegetation response to invasive species or to climate change.

##### 3.Deterministic epidemic models overestimate the basic reproduction number of observed outbreaks

**Authors:**Wajid Ali, Christopher E. Overton, Robert R. Wilkinson, Kieran J. Sharkey

**Abstract:** The basic reproduction number, $R_0$, is a well-known quantifier of epidemic spread. However, a class of existing methods for estimating this quantity from epidemic incidence data can lead to an over-estimation of this quantity. In particular, when fitting deterministic models to estimate the rate of spread, we do not account for the stochastic nature of epidemics and that, given the same system, some outbreaks may lead to epidemics and some may not. Typically, an observed epidemic that we wish to control is a major outbreak. This amounts to implicit selection for major outbreaks which leads to the over-estimation problem. We show that by conditioning a `deterministic' model on major outbreaks, we can more reliably estimate the basic reproduction number from an observed epidemic trajectory.

##### 1.Entropic contribution to phenotype fitness

**Authors:**Pablo Catalán, Juan Antonio García-Martín, Jacobo Aguirre, José A. Cuesta, Susanna Manrubia

**Abstract:** All possible phenotypes are not equally accessible to evolving populations. In fact, only phenotypes of large size, i.e. those resulting from many different genotypes, are found in populations of sequences, presumably because they are easier to discover and maintain. Genotypes that map to these phenotypes usually form mostly connected genotype networks that percolate the space of sequences, thus guaranteeing access to a large set of alternative phenotypes. Within a given environment, where specific phenotypic traits become relevant for adaptation, the replicative ability of a phenotype and its overall fitness (in competition experiments with alternative phenotypes) can be estimated. Two primary questions arise: how do phenotype size, reproductive capability and topology of the genotype network affect the fitness of a phenotype? And, assuming that evolution is only able to access large phenotypes, what is the range of unattainable fitness values? In order to address these questions, we quantify the adaptive advantage of phenotypes of varying size and spectral radius in a two-peak landscape. We derive analytical relationships between the three variables (size, topology, and replicative ability) which are then tested through analysis of genotype-phenotype maps and simulations of population dynamics on such maps. Finally, we analytically show that the fraction of attainable phenotypes decreases with the length of the genotype, though its absolute number increases. The fact that most phenotypes are not visible to evolution very likely forbids the attainment of the highest peak in the landscape. Nevertheless, our results indicate that the relative fitness loss due to this limited accessibility is largely inconsequential for adaptation.

##### 2.Statistical measures of complexity applied to ecological networks

**Authors:**Claudia Huaylla, Marcelo N Kuperman, Lucas A. Garibaldi

**Abstract:** Networks are a convenient way to represent many interactions among different entities as they provide an efficient and clear methodology to evaluate and organize relevant data. While there are many features for characterizing networks there is a quantity that seems rather elusive: Complexity. The quantification of the complexity of networks is nowadays a fundamental problem. Here, we present a novel tool for identifying the complexity of ecological networks. We compare the behavior of two relevant indices of complexity: K-complexity and Single value decomposition (SVD) entropy. For that, we use real data and null models. Both null models consist of randomized networks built by swapping a controlled number of links of the original ones. We analyze 23 plant-pollinator and 19 host-parasite networks as case studies. Our results show interesting features in the behavior for the K-complexity and SVD entropy with clear differences between pollinator-plant and host-parasite networks, especially when the degree distribution is not preserved. Although SVD entropy has been widely used to characterize network complexity, our analyses show that K-complexity is a more reliable tool. Additionally, we show that degree distribution and density are important drivers of network complexity and should be accounted for in future studies.